# MATH 221 Entire Course Statistics for Decision-Making NEW

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MATH 221 Entire Course Statistics for Decision-Making NEW
MATH 221 iLabs, Homework, Quizzes, Discussions Week 1-7, Final Exam, 100% Correct, Formulas Included…
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## MATH 221 Entire Course Statistics for Decision-Making NEW

MATH 221 Entire Course Statistics for Decision-Making NEW

This Course Includes ALL iLabs, Homework, Quizzes, Final Exam, and All Discussions ALL  100% Correct DeVry

Week 3 Quiz – 3 Sets

Week 5 Quiz – 3 Sets

Week 7 Quiz 4 Sets

All Quizzes and Final Exam Include Formulas in Excel and in Word that can be used if a numerical data is different  ALL 100% Correct.

This is a new course, but the most recent course is available here:

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MATH 221 iLab Week 2 NEW DeVry

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Statistical Concepts that you will learn after completing this iLab:

• Using Excel for Statistics
• Graphics
• Shapes of Distributions
• Descriptive Statistics
• Empirical Rule

Week 2 iLab Instructions-BEGIN

• Data have already been formatted and entered into an Excel worksheet.
• Obtain the data file for this lab from your instructor.
• The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. On page 6 of this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.
• Follow the directions below and then paste the graphs from Excel in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations.
• PLEASE NOTE that various versions of Excel may have slightly different formula commands. For example, some versions use =STDEV.S while other versions would use =STDEVS (without the dot before the last “S”).
• The completed iLab Word Document with your responses to the 11 questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab.

Week 2 iLab Instructions-END

Creating Graphs

Create a pie chart for the variable Car Color: Select the column with the Car variable, including the title of Car Color.  Click on Insert, and then Recommended Charts.  It should show a clustered column and click OK.  Once the chart is shown, right click on the chart (main area) and select Change Chart Type.  Select Pie and OK.  Click on the pie slices, right click Add Data Labels, and select Add Data Callouts.  Add an appropriate title.  Copy and paste the chart here. (4 points)

Create a histogram for the variable Height. You need to create a frequency distribution for the data by hand.  Use 5 classes, find the class width, and then create the classes.  Once you have the classes, count how many data points fall within each class. It may be helpful to sort the data based on the Height variable first.  Create a new worksheet in Excel by clicking on the + along the bottom of the screen and type in the categories and the frequency for each category.  Then select the frequency table, click on Insert, then Recommended Charts and choose the column chart shown and click OK.  Right click on one of the bars and select Format Data Series.  In the pop up box, change the Gap Width to 0.  Add an appropriate title and axis label.  Copy and paste the graph here. (4 points)

1. Type up a stem-and-leaf plot chart in the box below for the variable Money, with a space between the stems and the group of leaves in each line. Use the tens value as the stem and the ones value for the leaves.  It may be helpful to sort the data based on the Money variable first.

An example of a stem-and-leaf plot would look like this:

• 4  5  6  9  3
• 5  6  3  6
• 9  2

The stem-and-leaf plot shown above would be for data 4, 5, 6, 9, 3, 15, 16, 13, 16, 29, and 22. (4 points)

Calculating Descriptive Statistics

1. Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table.  Click in the top box and select all the data (including labels) from Height through Gender.  Also click on “new worksheet” and then OK.  On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values   Click on the down arrow next to Height in the Values box and select Value Field Settings.  In the pop up box, click Average then OK.  Type in the averages below.  Then click on the down arrow next to Height in the Values box again and select Value Field Settings.  In the pop up box, click on StdDev then OK.  Type the standard deviations below. (3 points)

All answers should be complete sentences.

What is the most common color of car for students who participated in this survey? Explain how you arrived at your answer. (5 points)

What is seen in the histogram created for the heights of students in this class (include the shape)? Explain your answer.  (5 points)

What is seen in the stem and leaf plot for the money variable (include the shape)? Explain your answer.  (5 points)

Compare the mean for the heights of males and the mean for the heights of females in these data. Compare the values and explain what can be concluded based on the numbers.   (5 points)

Compare the standard deviation for the heights of males and the standard deviation for the heights of females in the class. Compare the values and explain what can be concluded based on the numbers.  (5 points)

Using the empirical rule, 95% of female heights should be between what two values? Either show work or explain how your answer was calculated.  (5 points)

Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.   (5 points)

MATH 221 iLab Week 4 NEW DeVry

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This is a new lab, but the most recent lab is located here:

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Statistical Concepts:

• Probability
• Binomial Probability Distribution

Calculating Binomial Probabilities

• Open a new MINITAB worksheet.
• We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet.
• Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5.
• Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75.

Plotting the Binomial Probabilities

1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables.  Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’.  Paste those three scatter plots below.

Calculating Descriptive Statistics

• Open the class survey results that were entered into the MINITAB worksheet.
1. Calculate descriptive statistics for the variable where students flipped a coin 10 times. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to the coin. The output will show up in your Session Window. Type the mean and the standard deviation here.

Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.

1. List the probability value for each possibility in the binomial experiment that was calculated in MINITAB with the probability of a success being ½. (Complete sentence not necessary)
2. Give the probability for the following based on the MINITAB calculations with the probability of a success being ½. (Complete sentence not necessary)
3. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ½. Either show work or explain how your answer was calculated. Mean = np, Standard Deviation =
4. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¼ and compare to the results from question 5. Mean = np, Standard Deviation =
5. Calculate the mean and standard deviation (by hand) for the MINITAB created binomial distribution with the probability of a success being ¾ and compare to the results from question 6. Mean = np, Standard Deviation =
6. Explain why the coin variable from the class survey represents a binomial distribution.
7. Give the mean and standard deviation for the coin variable and compare these to the mean and standard deviation for the binomial distribution that was calculated in question 5. Explain how they are related. Mean = np, Standard Deviation =

MATH 221 iLab Week 6 NEW DeVry

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Statistical Concepts:

• Data Simulation
• Confidence Intervals
• Normal Probabilities

All answers should be complete sentences.

We need to find the confidence interval for the SLEEP variable.  To do this, we need to find the mean and then find the maximum error.  Then we can use a calculator to find the interval, (x – E, x + E).

First, find the mean.  Under that column, in cell E37, type =AVERAGE (E2:E36).  Under that in cell E38, type =STDEV (E2:E36).   Now we can find the maximum error of the confidence interval.  To find the maximum error, we use the “confidence” formula.  In cell E39, type =CONFIDENCE.NORM (0.05, E38, 35).  The 0.05 is based on the confidence level of 95%, the E38 is the standard deviation, and 35 is the number in our sample.  You then need to calculate the confidence interval by using a calculator to subtract the maximum error from the mean (x-E) and add it to the mean (x+E).

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. (6 points)
2. Give and interpret the 99% confidence interval for the hours of sleep a student gets. (6 points)
3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs. (6 points)
4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?  (9 points)
5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?  (9 points)
6. Find the mean and standard deviation of the DRIVE variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36). Assuming that this variable is normally distributed, what percentage of data would you predict would be less than 40 miles?  This would be based on the calculated probability.  Use the formula =NORM.DIST(40, mean, stdev,TRUE).  Now determine the percentage of data points in the dataset that fall within this range.  To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points.  That is the actual percentage.  How does this compare with your prediction?   (12 points)
7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Subtract the probabilities found through =NORM.DIST(70, mean, stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the “between” probability.  To get the probability of over 70, use the same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result from 1 to get “more than”.  Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set.  How do each of these compare with your prediction and why is there a difference?   (12 points)

MATH 221 iLab Week 2 DeVry

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Statistical Concepts:

• Using Minitab
• Graphics
• Shapes of Distributions
• Descriptive Statistics
• Empirical Rule

Data in Minitab

• Minitab is a powerful, yet user-friendly, data analysis software package. You can launch Minitab by finding the icon and double clicking on it. After a moment you will see two windows, the Session Window in the top half of the screen and the Worksheet or Data Window in the bottom half.
• Data have already been formatted and entered into a Minitab worksheet. Go to the eCollege Doc sharing site to download this data file. The names of each variable from the survey are in the first row of the Worksheet. This row has a background color of gray to identify it as the variable names. All other rows of the Minitab Worksheet represent a certain students’ answers to the survey questions. Therefore, the rows are called observations and the columns are called variables. Included with this lab, you will find a code sheet that identifies the correspondence between the variable names and the survey questions.
• Complete the questions after the Code Sheet and paste the Graphs from Minitab in the grey areas for question 1 through 3. Type your answers to questions 4 through 11 where noted in the grey areas. When asked for explanations, please give thorough, multi-sentence or paragraph length explanations. The completed iLab Word Document with your responses to the questions will be the ONE and only document submitted to the dropbox. When saving and submitting the document, you are required to use the following format: Last Name_ First Name_Week2iLab.

Code Sheet

Do NOT answer these questions. The Code Sheet just lists the variables name and the question used by the researchers on the survey instrument that produced the data that are included in the Minitab data file. This is just information. The first question for the lab is after the code sheet….

MATH 221 iLab Week 4 DeVry

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Statistical Concepts:

• Probability
• Binomial Probability Distribution

Calculating Binomial Probabilities

• Open a new MINITAB worksheet.
• We are interested in a binomial experiment with 10 trials. First, we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column, enter the numbers zero through ten to represent all possibilities for the number of successes. These numbers will end up in rows 1 through 11 in that first column. In column C2 enter the words ‘one fourth’ as the variable name. Pull up Calc > Probability Distributions > Binomial and select the radio button that corresponds to Probability. Enter 10 for the Number of trials: and enter 0.25 for the Event probability:. For the Input column: select ‘success’ and for the Optional storage: select ‘one fourth’. Click the button OK and the probabilities will be displayed in the Worksheet.
• Now we will change the probability of a success to ½. In column C3 enter the words ‘one half’ as the variable name. Use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.5.
• Finally, we will change the probability of a success to ¾. In column C4 enter the words ‘three fourths’ as the variable name. Again, use similar steps to that given above in order to calculate the probabilities for this column. The only difference is in Event probability: use 0.75.

Plotting the Binomial Probabilities

1. Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to ‘one fourth’ and X to ‘success’ by clicking on the variable name and using the “select” button below the list of variables.  Do this two more times and for graph 2 set Y equal to ‘one half’ and X to ‘success’, and for graph 3 set Y equal to ‘three fourths’ and X to ‘success’.  Paste those three scatter plots below…..

#### MATH 221 iLab Week 6 Devry

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Statistical Concepts:

• Data Simulation
• Discrete Probability Distribution
• Confidence Intervals

Calculations for a set of variables

• Open the class survey results that were entered into the MINITAB worksheet.
• We want to calculate the mean for the 10 rolls of the die for each student in the class. Label the column next to die10 in the Worksheet with the word mean. Pull up Calc > Row Statistics and select the radio-button corresponding to Mean. For Input variables: enter all 10 rows of the die data. Go to the Store result in: and select the mean Click OK and the mean for each observation will show up in the Worksheet.
• We also want to calculate the median for the 10 rolls of the die. Label the next column in the Worksheet with the word median. Repeat the above steps but select the radio-button that corresponds to Median and in the Store results in: text area, place the median

Calculating Descriptive Statistics

• Calculate descriptive statistics for the mean and median columns that where created above. Pull up Stat > Basic Statistics > Display Descriptive Statistics and set Variables: to mean and median. The output will show up in your Session Window. Print this information.

Calculating Confidence Intervals for one Variable

• Open the class survey results that were entered into the MINITAB worksheet.
• We are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window.
• We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99. Short Answer Writing Assignment

All answers should be complete sentences.

MATH 221 Quiz Week 3 ALL Answers are 100% Correct 3 Sets

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These quizzes include formulas in Excel and in Word that can be used if numeric data is different from the one listed below.

Another, the most recent quiz is available here:

https://www.hiqualitytutorials.com/product/math-221-quiz-week-3-recent-devry/

1. These quizzes include formulas in Excel and in Word that can be used if numeric data is different from the one listed below.
1. Use the Venn diagram to identify the population and the sample.

Choose the correct description of the population.

A.  The number of home owners in the state
B.  The income of home owners in the state who own a car
C.  The income of home owners in the state
D.  The number of home owners in the state who own a car

Choose the correct description of the sample

A.  The income of home owners in the state who own a car
B.  The income of home owners in the state
C.  The number of home owners in the state who own a car
D.  The number of home owners in the state

1. Determine whether the variable is qualitative or quantitative.

Favorite sport

Is the variable qualitative or quantitative?

A.  Qualitative
B.  Quantitative

1. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below.

43  50  10  91  76  35  64  36  42  72  53  62  35  74  50
72  36  28  38  61  48  63  35  41  22  36  50  46  85  13

To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and highest 10% of the entries, and find the mean of the remaining entries.  Complete parts (a) through (c).

(a) Find the 10% trimmed mean for the data.
The 10% trimmed mean is.  (Round to the nearest tenth as needed.)
(b) Compare the four measures of central tendency, including the midrange.
Mean =  (Round to the nearest tenth as needed.)
Median =
Mode =  (Use a comma to separate answers as needed.)
Midrange =  (Round to the nearest tenth as needed.)

(c) What is the benefit of using a trimmed mean versus using a mean found using all data entries?

A.  It simply decreases the number of computations in finding the mean.
B.  It permits the comparison of the measures of central tendency.
C.  It permits finding the mean of a data set more exactly.
D.  It eliminates potential outliers that could affect the mean of the entries.

1. Construct a frequency distribution for the given data set using 6 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?

Amount (in dollars) spent on books for a semester

457  146  287  535  442  543  46  405  496  385  517  56  33  132  64
99  378  145  30  419  336  228  376  227  262  340  172  116  285

Complete the table, starting with the lowest class limit.  Use the minimum data entry as the lower limit of the first class. (Type integers or decimals rounded to the nearest thousandth as needed.)

Which class has the greatest frequency?
The class with the greatest frequency is from  to.
Which class has the least frequency?
The class with the least frequency is from to.

1. Identify the data set’s level of measurement.

The nationalities listed in a recent survey (for example, American, German, or Brazilian)

A.  Nominal
B.  Ordinal
C.  Interval
D.  Ratio

1. Explain the relationship between variance and standard deviation. Can either of these measures be negative?

A.  The standard deviation is the negative square root of the variance. The standard deviation can be negative but the variance can never be negative.
B.  The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative.  Squared deviations can never be negative.
C.  The variance is the negative square root of the standard deviation. The variance can be negative but the standard deviation can never be negative.
D.  The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative.  Squared deviations can never be negative.

1. For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation.

The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following Monday.

Hours spent watching TV, x   0          1          2          3          3          5

Test score, y                            98        90        84        74        93        65

(a) Choose the correct scatter plot below.

(b) The correlation coefficient r is (Round to three decimal places as needed)
(c) Which of the following best describes the type of correlation that exists between number of hours spent watching television and test scores?

A.  Strong negative linear correlation
B.  No linear correlation
C.  Weak negative linear correlation
D.  Strong positive linear correlation
E.  Weak positive linear correlation

1. Suppose a survey of 526 women in the United States found that more than 70% are the primary investor in their household. Which part of the survey represents the descriptive branch of statistics?

Choose the best statement of the descriptive statistic in the problem.

A.  There is an association between the 526 women and being the primary investor in their household.
B.  526 women were surveyed.
C.  70% of women in the sample are the primary investor in their household.
D.  There is an association between U.S. women and being the primary investor in their household.
Choose the best inference from the given information.

A.  There is an association between the 526 women and being the primary investor in their household.
B.  There is an association between U.S. women and being the primary investor in their household.
C.  70% of women in the sample are the primary investor in their household
D.  526 women were surveyed.

1. Identify the sampling technique used.

A community college student interviews everyone in a particular statistics class to determine the percentage of students that own a car.

A.  Random
B.  Cluster
C.  Convenience
D.  Stratified
E.  Systematic

1. Use the frequency polygon to identify the class with the greatest, and the class with the least frequency.

What are the boundaries of the class with the greatest frequency?

A.  25.5-30.5
B.  25-31
C.  26.5-29.5
D.  28-31

What are the boundaries of the class with the least frequency?

A.  10-13
B.  5-11.5
C.  7-13
D.  5-12.5

1. Determine whether the given value is a statistic or a parameter

In a study of all 2377 students at a college, it is found that 35% own a computer

Choose the correct statement below.

A.  Parameter because the value is a numerical measurement describing a characteristic of a population.
B.  Statistic because the value is a numerical measurement describing a characteristic of a population.
C.  Statistic because the value is a numerical measurement describing a characteristic of a sample.
D.  Parameter because the value is a numerical measurement describing a characteristic of a sample.

1. Compare the three data sets

(a) Which data set has the greatest sample standard deviation?

A.  Data set (iii), because it has more entries that are farther away from the mean
B.  Data set (ii), because it has two entries that are far away from the mean.
C.  Data set (i), because it has more entries that are close to the mean.

Which data set has the least sample standard deviation?

A.  Data set (i), because it has more entries that are close to the mean.
B.  Data set (ii), because it has less entries that are farther away from the mean.
C.  Data set (iii), because it has more entries that are farther away from the mean.

(b) How are the data sets the same? How do they differ?

A.  The three data sets have the same standard deviations but have different means.
B.  The three data sets have the same mean, median and mode but have different standard deviation.
C.  The three data sets have the same mean and mode but have different medians and standard deviations.
D.  The three data sets have the same mode but have different standard deviations and means

1. Decide which method of data collection you would use to collect data for the study.

A study of the effect on the human digestive system of a popular soda made with a caffeine substitute.

A.  Observational Study
B.  Simulation
C.  Survey
D.  Experiment

1. Use the given frequency distribution to find the:
• (a) Class width
• (b) Class midpoint of the first class
• (c) Class boundaries of the first class

A.  (a) 4 (b) 137.5 (c) 134.5-139.5
B.  (a) 5 (b) 137 (c) 135-139
C.  (a) 5 (b) 137 (c) 134.5-139.5
D.  (a) 4 (b) 137.5 (c) 135-139

1. Consider the following sample data values.

5          14        15        21        16        13        9          19

(a) Calculate the range
(b) Calculate the variance
(c) Calculate the standard deviation

a.  The range is. (Type an integer or a decimal)
b.  The sample variance is. (Type an integer or decimal rounded to two decimal places as needed)
c.  The sample standard deviation is. (Type an integer or decimal rounded to two decimal places as needed)

1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.  (the pair of variables have a significant correlation.)  Then use the regression equation to predict the value of y for each of the given x-values, if meaningful.  The number of hours 6 students spent for a test and their scores on that test are shown below.

Find the regression equation.

^

Y = x + () (Round to three decimal places as needed)

Choose the correct graph below.

(a)  Predict the value of y for x = 4. Choose the correct answer below.

1. 1
2. 8
3. 8
4. Not meaningful
• (b) Predict the value of y for x = 4.5. Choose the correct answer below.
1. 1
2. 8
3. 0
4. Not meaningful

(c)  Predict the value of y for x = 12.  Choose the correct answer below.

1. 8
2. 1
3. 0
4. Not meaningful

(d) Predict the value of y for x = 2.5. Choose the correct answer below.

A.  57.8
B.  47.8
C.  111.0
D.  Not meaningful

1.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 20 students. The scores are given below.
27 15 39 43 23 14 49 33 57 35
36 14 13 38 22 24 22 48 14 23

1. Suppose that a study based on a sample from a targeted population shows that people at a pizza restaurant are hungrier than people at a coffee shop.
A) make an inference based on the results of this study.
B) what might this inference incorrectly imply?

3.Decide which method of data collecting you would use to collect data for the study below:
A study of how fast a virus would spread in a school of fish.

1. Identify the sampling technique used:
The name of 50 contestants are written on 50 cards. The cards are placed in a bag, and three names are picked from the bag.

5.In a poll of 1002 women in a country were asked whether they favor or oppose of the use of federal tax dollars to fund medical research using stem cells obtained from embryos. Among the women, 48% said they were in favor.

1. Identify the data set’s level of measurement.
The years the summer Olympics were held in a particular country

7.Use the frequency histogram to answer each question.
A) determine the # of classes
B) estimate the frequency of the class with the least frequency.
C) estimate the frequency of the class with the greatest frequency.
D) determine the class width.

8.The data represents the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include midpoints, relative frequencies, and cumulative frequencies. Which class had the greatest and least frequency?

1. Given a data set, how do you know whether to calculate σ or s?

10.Compare the three data sets on the right.

11.Use the given minimum and maximum data entries and the number of classes to find class width, lower class limits, and upper class limits.
min = 9, max = 83, classes = 6

12.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city.

13.For the following data (a) display the data in a scatter plat, (b) calculate the correlation coefficient r, and (c) make a conclusion about the type of correlation.
The ages (in years) of 6 children and the number of words in their vocabulary.

 Age, X 1 2 3 4 5 6 Vocabulary Size 350 950 1200 1700 2250 2600

14.Determine whether the underlined numerical value is a parameter or a statistic. In a poll of a sample of 12,000 adults, in a certain city, 12% said they left for work before 6am.

15.Both data sets have a mean of 225. One has a SD of 16 and the other has an SD of 24.

16.Use the Venn diagram to identify the population and the sample.

17.Determine whether the variable is qualitative or quantitative. Breed of cat.

18.Use the relative frequency histogram below to complete each part.
A) identify the class with the greatest and the class with the least frequency.
B) approximate the greatest and least relative frequencies.
C) approximate the relative frequency of the second class.

19.Use the given frequency distribution to find the:
A) class width
B) class midpoint of the first class
C) class boundaries of the first class.

 Height (in inches) Class Frequency 50-52 5 53-55 8 56-58 12 59-61 13 62-64 11

20.For the following data (a) display the data in a scatter plot, (b) calculate the correlation coefficient r, and (c) make a conclusion about that type of correlation.
The number of hours 6 students watched television during the weekend and the scores of each student who took a test the following monday.

 Hours spent Watching TV 0 1 2 3 3 5 Test Score 98 89 86 70 81 66

21.Explain the relationship below between variance and standard deviation. Can either of these measures be negative?

22.Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are shown below.
44        50        10        91        77        35        64        36        43        72        54        62        35        75        50

72        36        29        39        61        49        63        35        41        21        36        50        47        86        13

To find the 10% trimmed mean of a data set, order the data, delete the lowest and highest 10% of the entries

23.Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (the pair of variables have a significant correlation.) then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

1. Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning.
the average grade on the midterm exam in a certain math class of 50 students was an 88.

25.Suppose that a study based on a sample from a targeted population shows that people who own a fax machine have more money than people who do not.
A) Make an inference based on the results of this study.
B) What might this inference incorrectly imply?

1. Identify the data set’s level of measurement.
The average daily temperatures (in degrees Fahrenheit) on five randomly selected days.
23, 33, 28, 34, 35

27.Identify the sampling technique used.
The name of 100 contestants are written on 100 cards. The cards are placed in a bag, and three names are picked from the bag.

28.Which method of data collection should be used to collect data for the following study.
The average weight of 175 students in a high school.

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1. Sixty percent of households say they would feel secure if they had \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

(a) Find the probability that the number that say they would feel secure is exactly five

P(5) = (Round to three decimal places as needed)

(b) Find the probability that the number that say they would feel secure is more than five.

P(x>5) = (Round to three decimal places as needed)

(c) Find the probability that the number that say they would feel secure is at most five.

P(x≤5) = (Round to three decimal places as needed)

1. Suppose 80% of kids who visit a doctor have a fever, and 25% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

The probability is. (Round to three decimal places as needed)

1. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 90, p = 0.8

The mean, µ is (Round to the nearest tenth as needed)

The variance, σ2, is (Round to the nearest tenth as needed)

The standard deviation, σ is (Round to the nearest tenth as needed)

1. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is E.

The probability that the highest level of education for an employee chosen at random is E is.  (Round to the nearest thousandth as needed)

1. A company that makes cartons finds that the probability of producing a carton with a puncture is 0.05, the probability that a carton has a smashed corner is 0.09, and the probability that a carton has a puncture and has a smashed corner is 0.005. Answer parts (a) and (b) below.
• Are the events “selecting a carton with a puncture” and “selecting a carton with a smashed corner” mutually exclusive?
• A. No, a carton can have a puncture and a smashed corner.
1. Yes, a carton can have a puncture and a smashed corner
2. Yes, a carton cannot have a puncture and a smashed corner
3. Mo, a carton cannot have a puncture and a smashed corner
• If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner.

The probability that a carton has a puncture or a smashed corner is 0.135.  (Type an integer or a decimal.  Do not round)

1. Given that x has a Poisson distribution with µ = 8, what is the probability that x = 3?

P(3) ≈ (Round to four decimal places as needed)

1. Perform the indicated calculation.

= (Round to four decimal places as needed)

1. A frequency distribution is shown below. Complete parts (a) through (d)

The number of televisions per household in a small town

Televisions      0          1          2          3

Households     26        448      730      1400

a. Use the frequency distribution to construct a probability distribution

X                     P(x)
0
1
2
3
(Round to the nearest thousandth as needed)

b. Graph the probability distribution using a histogram. Choose the correct graph of the distribution below.

Describe the histogram’s shape.  Choose the correct answer below.

A. Skewed right
B. Skewed left
C. Symmetric

c.  Find the mean of the probability distribution
µ = (round to the nearest tenth as needed)
Find the variance of the probability distribution
σ2 = (round to the nearest tenth as needed)
Find the standard deviation of the probability distribution
σ = (round to the nearest tenth as needed)

Interpret the results in the context of the real-life situation.

d. The mean is 2.3, so the average household has about 3 television. The standard deviation is 0.6 of the households differ from the mean by no more that about 1 television
A. The mean is 0.6, so the average household has about 1 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television
B. The mean is 2.3, so the average household has about 2 television. The standard deviation is 0.8 of the households differ from the mean by no more that about 1 television

C. The mean is 0.6, so the average household has about 1 television. The standard deviation is 2.3 of the households differ from the mean by no more that about 3 television

1. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman is 650 carries a mutation of the BRCA gene.  Nine out of 10 women with this mutation develop breast cancer. a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is. (Round to one decimal place as needed)

b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.

The probability that a randomly selected woman will carry the gene nutation and develop breast cancer is. (Round to four decimal places as needed)

c. Are the events of carrying this mutation and developing breast cancer independent or dependent?

A. Dependent
B. Independent

1. Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution.  Complete parts (a) through (e)

X                     0          1          2          3          4          5          6          7          8

P(x)                 0.04     0.04     0.06     0.06     0.12     0.24     0.23     0.14     0.07

a. Use the probability distribution to find the mean of the probability distribution
µ= (Round to the nearest tenth as needed)
b. Use the probability distribution to find the variance of the probability distribution
σ2= (Round to the nearest tenth as needed)
c. Use the probability distribution to find the standard deviation of the probability distribution
2.0 (Round to the nearest tenth as needed)
d. Use the probability distribution to find the expected value of the probability distribution
4.9 (Round to the nearest tenth as needed)
e. Interpret the results

A. The expected number of questions answered correctly is 2.0 with a standard deviation of 4.9 questions.
B. The expected number of questions answered correctly is 4 with a standard deviation of 2.0 questions.
C. The expected number of questions answered correctly is 4.9 with a standard deviation of 0.04 questions.
D. The expected number of questions answered correctly is 4.9 with a standard deviation of 2.0 questions.

1. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a multiple of 5 between 21 and 49

The sample space is {}  (Use a comma to separate answers as needed.  Use ascending order)

There are outcome(s) in the sample space.

1. Decide if the events shown in the Venn diagram are mutually exclusive.

Are the events mutually exclusive?

A.  Yes
B.  No

1. Determine whether the random variable is discrete or continuous.

a. The number of free-throw attempts before the first shot is made
b. The weight of a T-bone steak
c. The number of bald eagles in the country
d. The number of points scored during a basketball game
e. The number of hits to a website in a day

(a) Is the number of free-throw attempts before the first shot is made discrete or continuous?

A. The random variable is continuous
B, The random variable is discrete

(b) Is the weight of a T-bone steak discrete or continuous?

A. The random variable is discrete
B. The random variable is continuous

(c) Is the number of bald eagles in the country discrete or continuous?

A. The random variable is discrete
B. The random variable is continuous

(d) Is the number of points scored during a basketball game discrete or continuous?

A. The random variable is discrete
B. The random variable is continuous

(e) Is the number of hits to a website in a day discrete or continuous?

A. The random variable is discrete
B. The random variable is continuous

14.  A survey asks 1100 workers: Has the economy forced you to reduce the amount of vacation you plan to take this year?” Fifty-six percent of those surveyed say they are reducing the amount of vacation.  Twenty workers participating in the survey are randomly selected.  The random variable represents the number of workers who are reducing the amount of vacation.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

A. Yes
B. No

What is a success in this experiment?

A.  Selecting a worker who is reducing the amount of vacation
B.  Selecting a worker who is not reducing the amount of vacation
C.  This is not a binomial experiment

Specify the value of n.  Select the correct choice and fill in any answer boxes in your choice

A.  N=
B. This is not a binomial experiment

Specify the value of p.  Select the correct choice below and fill in any answer boxes in your choice.

A.  P= (Type an integer or a decimal)
B.  This is not a binomial experiment

Specify the value of q.  Select the correct choice below and fill in any answer boxes in your choice.

A.  Q= (Type an integer r a decimal)
B.  This is not a binomial experiment

List the possible values of the random variable x

A.  X=0, 1, 2,…, 20
B.  X=1, 2, 3,…, 1100
C.  1, 2,…, 20
D.  This is not a binomial experiment

15.  Determine whether the distribution is a discrete probability distribution.

Is the distribution a discrete probability distribution?  Why?  Choose the correct answer below.

A.  Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive
B.  No, because the total probability is not equal to 1
C.  Yes, because the distribution is symmetric
D.  No, because some of the probabilities have values greater than 1 or less than 0

16.  The table below shows the results of a survey that asked 2872 people whether they are involved in any type of charity work. A person is selected at random from the sample.  Complete parts (a) through (e).

Frequency       Occasionally    Not at all         Total

Male                226                  455                  793                  1474
Female             206                  450                  742                  1398
Total                432                  905                  1535                2872

a.  Find the probability that the person is frequently or occasionally involved in charity work

P(being frequently involved or being occasionally involved) =  (Round to the nearest thousandth as needed)
b.  Find the probability that the person is male or frequently involved in charity work

P(being male or being frequently involved) =
c.  Find the probability that the person is female or not involved in charity work at all

P(being female or not being involved) = 0.763 (Round to the nearest thousandth as needed)
d. Find the probability that the person is female or not frequently involved in charity work

P(being female or not being frequently involved) = (Round to the nearest thousandth as needed)
e.  Are the events “being female” and “being frequently involved in charity work” mutually exclusive?

A.  No, because 206 females are frequently involved in charity work.
B.  Yes, because no females are frequently involved in charity work.
C.  Yes, because 206 females are frequently involved in charity work.
D.  No, because no females are frequently involved in charity work.

17.  For the given pair of events, classify the two events as independent or dependent.

Swimming all day at the beach
Getting a sunburn

A.  The two events are independent because the occurrence on one does not affect the probability of the occurrence of the other.
B.  The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
C.  The two events are independent because the occurrence of one affects the probability of the occurrence of the other.
D.  The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.

18.  Outside a home, there is a 9-key keypad with letters A, B, C, D, E, F, G, H, and I that can be used to open the garage if the correct nine-letter code is entered. Each key may be used only once.  How many codes are possible?

The number of possible codes is.

19.  Determine the number of outcomes in the event. Decide whether the event is a simple event or not.

A computer is used to select randomly a number between 1 and 9, inclusive.  Event C is selecting a number less than 5.

Event has outcome(s)
Is the event a simple event?

1.Decide whether the random variable x is discrete or continuous
X represents the number of home theater systems sold per month at an electronics store.

1.Evaluate the given expression and express the results using the usual format for writing numbers (instead of scientific notation
36C2

2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
N = 80, p = 0.4

2.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
N = 128, p = 0.36

1. A new phone answering system for a company is capable of handling four calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to one every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10 – minute period more calls will arrive than the system can handle?

3.Suppose 90% of kids who visit a doctor have a fever, and 35% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

1. You randomly select one card from a standard deck. Event A is selecting a nine. Determine the number of outcomes in event A. then decide whether the event is a simple event or not.

4.A frequency distribution is shown below. Complete parts (a) through €.
The number of dogs per household in a small town.

 Dogs 0 1 2 3 4 5 Households 1295 416 163 47 27 12

5.22% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. If convenient, use technology to find the probabilities.

5.The table below shows the results of a survey that asked 2870 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e).

6.The table below shows the results of a survey that asked 2885 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e).

6.Identify the sample space of the probability experiment and determine the number of outcomes in a sample space.
Randomly choosing an even number between 10 and 20, inclusive.

7.Students in a class take a math quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distributions. Complete parts (a) through €

7.Determine whether the events E and F are independent or dependent. Justify your answer.

8.A certain lottery has 29 numbers. In how many different ways can 4 of the numbers be selected? (assume that order of selection is not important.)

8.Determine the required value of the missing probability to make the distribution a discrete probability distribution

9.Determine whether the distribution Is a discrete probability distribution.

9.The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution.

10.Decide if the events are mutually exclusive.
Event A: Randomly selecting someone who is married
Event B: Randomly selecting someone who is a bachelor

10.A standard deck of cards contains 52 cards. One card is selected from the deck.
A)  compute the probability of randomly selecting a six or three.
B) compute the probability of randomly selecting a six, three, or king.
C) compute the probability of randomly selecting an eight or club.

11.A survey asks 1200 workers, “has the economy forced you to reduce the amount of vacation you plan to take this year?” 52% of those surveyed say they are reducing the amount of vacation. Ten workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p and q.

11.A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty eight percent of the ART pregnancies resulted in multiple births.

12.Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen random is E.

12.A golf-course architect has four linden trees, five white birch trees, and two bald cypress tress in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?

13.Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.

13.Decide if the events are mutually exclusive.
Event A) Receiving a phone call from someone who opposes all cloning
Event B) Receiving a phone call from someone who approves of cloning sheep.

14.Determine whether the events E and F are independent or dependent. Justify your answer.

14.47% of men consider themselves a professional baseball fan. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability tha the number who consider themselves baseball fans is (a) 8, (b) at least 8, and (c) less than eight. If convenient, use technology to find the probabilities.

15.Suppose 60% of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

15.Given that x has a Poisson distribution with ᶙ = 8, what is the probability that x = 1?

16.Perform the indicated calculation.

16.Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding a car driven by someone else?” find the following probabilities of responses of college students from the survey chosen at random.

17.A frequency distribution is shown below. Complete parts (a) through (d).
The number of televisions per household in a small town.

 Televisions 0 1 2 3 Households 2 443 723 1409

17.About 30% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

18.A study found that 37% of the assisted reproductive technology (ART) cycles resulted in pregnancies. 24% of the ART pregnancies resulted in multiple births.
A) find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth.
B) find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
C) would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?

1. You randomly select one card from a standard deck. Event A is selecting a three. Determine the number of outcomes in event A. then decide whether the event is a simple event or not.

19.A company that makes cartons finds the probability of producing a carton with a puncture is 0.07, the probability that a carton has a smashed corner is 0.1, and the probability that a carton has a puncture and has a smashed corner is 0.007. answer parts (a) and (b)

19.Determine whether the random variable is discrete or continuous.
a. the # of bald eagles in the country.
b. the weight of a t-bone steak.
c. the time it takes for a light bulb to burn out.
d. the number of fish caught during a fishing tournament.
e. the distance a baseball travels in the air after being hit.

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1. A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that don’t wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?

Tires that wear out by …miles will be replaced free of charge.

1. Find the indicated z-score shown in the graph to the right.

The z-score is

1. A researcher wishes to estimate, with 95% confidence, the amount of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
a) find the minimum sample size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access(b) no preliminary estimate is available. Find the minimum sample size needed.a) =
b) =
2. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 221 milligrams per deciliter and a standard deviation of 37.7 milligrams per deciliter.
(a) what percent of men have a total cholesterol level less than 228 milligrams per deciliter of blood?
(b) if 251 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 264 milligrams per deciliter of blood?
a) =
b) =
3. Find the z-score that has a 12.1% of the distribution’s area to it’s left.
4. A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming σ = 18.1? suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?
99% =
90% =
how does the decrease in confidence affect the sample size required?
5. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.054
6. In a survey of 3076 adults, 1492 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.
With 99% confidence, it can be said that the…
7. Assume the random variable x is normally distributed with mean u = 89 and standard deviation o = 4. Find the indicated probability. P(76<x<82)
1. Find the margin of error for the given values of c,s, and n.
c = .90, s = 3.1, n =49
1. Find the critical value Tc for the confidence level c = .90 and sample size n = 29.
Tc =
2. The mean height of women in a country (ages 20-29) is 63.9 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume o = 2.91
1. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed with a mean of 67.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (A) through (C).
(a) the probability that his height is less than 68 inches.
(b) the probability that his height is between 68-71 inches.
(c) the probability that his height is more than 71 inches.
1. For the standard normal distribution shown on the right, find the probability of z occurring in the region.

Probability =
1. Find the indicated probability using the standard normal distribution.
(P – 1.35 < z < 1.35) =
1. Find the margin of error for the given values of c, s, n.
c = 0.98, s = 5, n = 6
1. The systolic blood pressures of a sample of adults are normally distributed with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 122 millimeters of mercury, 113 millimeters of mercury, 106 millimeters of mercury, and 128 millimeters of mercury. The graph of the standard normal distribution is below. Complete parts a – c.

(a) Match the values with the letters a/b/c/d.
A =
B =
C =
D =
(b) Find the z-scores that corresponds to each value
A =
B =
C =
D =

(c) Determine if any of the values are unusual, and classify them as either unusual or very unusual.

1. You are given a sample mean and standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 60 home theater systems has a mean price of \$134.00 and a standard deviation is \$19.60The 90% confidence interval is
The 95% confidence interval isInterpret the results.

Answer: With 90% confidence, it can be…

1. The monthly incomes for 12 randomly select people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.

Mean =
Standard Deviation =
99% confidence interval =

1. What is the total area under the normal curve?
2. A population has a mean u = 82 and a standard deviation o = 36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 81

22.  The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.4 hours and a standard deviation of 0.38 hour. Random sample of size 25 and 37 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?

Mean of distribution =
Standard deviation of distribution =

If the sample size is n = 37, find the mean and standard deviation.

Mean =
Standard deviation =

What happens to the mean and standard deviation of the distribution of sample means as the size of the sample increases?
Answer: The mean stays the same, the but standard deviation decreases.

23.  Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph.

1.Find the probability and interpret the results. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialist is about \$64,000. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than \$62,000? Assume σ = \$5,700

1.Use the standard normal table to find the z-score that corresponds to the cumulative area 0.1084. if the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z scores.

1.In a survey of women in a certain country (ages 20-29), the mean height was 63.8 inches with a standard deviation of 2.94 inches. Answer the following questions about the specified normal distribution.
A) what height represents the 99th percentile?
B) what height represents the first quartile?

2.Find the probability and interpret the results. If convenient, use technology to find the probability.
The population mean annual salary for environmental compliance specialists is about \$61,000. A random sample of 42 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than \$57,500? Assume σ = \$6,000

2.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

1. In a recent year, scores on a standardized test for high school students with a 3.50 – 4.00 GPA were normally distributed with a mean of 39.3 and a standard deviation of 2.3. A student with a 3.50 – 4.00 GPA who took the standardized test Is randomly selected.
2. Find the z-scores for which 5% of the distribution area lies between –z and z.
3. Use the central time limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.
The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 106 pounds and a standard deviation of 39.7 pounds. Random samples of size 19 are drawn from this population and the mean of each sample is determined.
4. The mean height of women in a country (ages 20-29) is 64.2 inches. A random sample of 70 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume σ = 2.94
5. The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 202 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter.

A) The % of the men that have a total cholesterol level less than 213 milligrams per deciliter of blood is B) of the 259 men… would be expected to have a total cholesterol level greater 257 milligrams per deciliter of blood.

5.A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 2% of the true proportion.

A – What is the minimum sample size needed using a prior study that found that 52% of the respondents said they have high-speed internet access? =
B – Minimum sample size needed? =5.

Find the margin of error for the given clues of c,s, and n.
c = 0.95, s = 2.7, n = 36

5.If a z-score is zero, which of the following is true?
5.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected is from the shaded area.

6.Find the z-score that has 2.5% of the distribution area to it’s right.

6.Find the z-score that has 28.1% of the distribution’s area to its left

7.Find the margin of error for the given values of c,s, and n.
C = 0.95, s = 3.1, N = 100

1. Find the critical value Tc for the confidence level c = 0.90 and sample size of n = 17
2. In a survey of women in a certain country (ages 20-29) the mean height was 64.1 inches with a standard deviation of 2.94 inches. Answer the following questions about the specified normal distribution
A) what height represents the 98th percentile?
B) what height represents the first quartile

8.The SAT is an exam used by colleges and universities to evaluate the undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 1510 and the standard deviation was 315. The test scores of 4 random students are as follows: 1946, 1266, 2199, and 1407

(A) Without converting to z-scores, match the values with the letters a/b/c/d on the given graph of the standard normal distribution.
(B) Find the z-scores that corresponds to each value
C) Determine whether any of the values are unusual.

1. A beverage company uses a machine to fill one-liter bottles with water. Assume that the population of volumes is normally distributed. (a) the company wants to estimate the mean value of water the machine is putting in the bottles within 1 milliliter. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 4 milliliters.
(b) Repeat part (a) using an error tolerance of 3 milliliters. Which error tolerance requires a larger sample size?

(A) the minimum sample size required for an error tolerance of 1 is… bottles
(b) the minimum sample size required for an error tolerance of 3 is …bottles

The error tolerance of … requires a larger sample size. As the error size decreases, a larger sample must be taken to obtain sufficient information from the population to ensure accuracy.

1. A population has a mean u = 83 and a standard deviation o = 23. Find the mean and standard deviation of sample means with sample size n = 247.
2. The monthly income for 12 randomly selected people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.

9.Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph.

1. Find the indicated probability using standard normal distribution.
P(-0.78 < Z < 0.78)
10.Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 5 inches. Assume the variable x is normally distributed.
(a) what percent of fish are longer than 13 inches?
(b) if 500 fish are randomly selected, how many would be shorter than 9 inches?
2. Find the margin of error for the given values of c,s, and n.
C = 0.90, s = 3.2, n =100
3. A researcher wishes to estimate, with 90% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
A – Find the minimum sample size needed using a study of 46%
B – No estimate is available. Find the minimum sample size.

11.A doctor wants to estimate the HDL cholesterol of all 20-29 year old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming o = 17.3? suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size?

11.The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 121 millimeters of mercury, 114 millimeters of mercury, 105 millimeters of mercury, and 126 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below.

a….

b….

1. The unusual value(s) is/are …. The very unsual(s) is/are …
2. In a recent year, scores on a standardized test for high school students with a 3.50 to 4.00 gpa were normally distributed, with a mean of 39.7 and a standard deviation of 2.5. A student with a 3.50 to 4.00 gpa who took the standardized test is randomly selected.A. find the probability that the student’s test score is less than 35.
B. find the probability that the student’s test score is between 35.7 and 43.7
C. find the probability that the student’s test score is more than 41.7
3. Find the margin of error for the given values of c,s, and n.
C = 0.95, S = 4, N = 27
4. Assume the random variable x is normally distributed with mean u = 50 and standard deviation o = 7. Find the indicated probability. P(X>39)
12. The systolic blood pressures of a sample of adults are normally distributed, with a mean pressure of 115 millimeters of mercury and a standard deviation of 3.6 millimeters of mercury. The systolic blood pressures of four adults selected at random are 119 millimeters of mercury, 113 millimeters of mercury, and 127 millimeters of mercury. The graph of the standard normal distribution is shown to the right. Complete parts (a) through (c) below.
• Without converting to z-scores, match the values with the letters A, B, V, and D on the given graph above of the standard normal distribution.
• Find the z-score that corresponds to each value and check your answers to part (a)
• Determine whether any of the values are unusual, and classify them as either unusual or very unusual. Select the correct answer below and, if necessary, fill in the answer box(es) within your choice….
1. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between corresponding z-scores. If convenient, use technology to find the z-score. 0.049.
2. Find the critical value t for the confidence level c =0.99 and sample size n = 13.

Click the icon to view the t-distribution table.

1. Find the margin of terror for the given values of c,s, and n.
C = 0.95, S = 3.9, N = 26

14 For the standard normal distribution shown on the right, find the probability of z occurring in the indicated region. -0.62

1. You are given the sample mean and sample and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 36 gas grills has a mean price of \$637.60 and a standard deviation of \$55.80

14.Use the central limit theorem to find the mean and the standard error of the mean of the indicated sampling distribution. The sketch a graph of the sampling distribution.

The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 39.1 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined.

1. What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

15.Find the indicated probability using the standard normal distribution.
P (-0.21 < z < 0.21)

1. You are given the sample mean and the sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct confidence intervals.
A random sample of 40 home theater systems has a mean price of \$1111.00 and a standard deviation is \$15.50
2. A population has a mean u = 80 and a standard deviation o = 30. Find the mean and standard deviation of a sampling distribution of sample means with sample size 250.
3. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown above. Assume the population is normally distributed.

16.A population has a mean of 75 and standard deviation of 36. Find the mean/sd of a sampling distribution of sample means with sample size n = 81.

Mean = 75
Standard deviation = 4

17.Find the indicated probability using the standard normal distribution.
P ( -0.37 < z < 0.37)
17. Find the indicated z-scores shown in the graph.

1. In a survey of 3455 adults, 1467 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.

18.The amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.8 hours and a standard deviation of 0.33 hour. Random sample of size 25 and 38 are drawn from the population and the mean of each sample is determined. What happens to the mean and the standard deviation of the distribution of sample means as the size of the sample increases?

If the sample size n = 25, find the mean and standard deviation of the distribution of sample means.

1. Find the margin of error for the given values of c,s, and n.
C = 0.98, s = 5, n = 24
2. A researcher wishes to estimate, with 99% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 4% of the true proportion.
A) find the minimum sample size needed, using a prior study that found that 54% of the respondents said that they have high speed internet access.
B) no preliminary estimate is available. Find the minimum sample size needed.

19.In a survey of women in a certain country (ages 20-29), the mean height was 63.4 inches with a standard deviation of 2.87 inches. Answer the following questions about the specified normal distribution.
A) what height represents the 95th percentile?
B) what height represents the first quartile

1. In a normal distribution, which is greater, the mean or the median?

Find the indicated z-score shown in the graph

1. In a normal distribution, which is greater, the mean or the median? Explain.
20. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider?
A random sample of 31 gas grills has a mean price of \$631.70 and a standard deviation of \$55.10
2. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown on the right. Assume the population is normally distributed.
3. A beverage company uses a machine to fill cone-liter bottles (see figure). Assume that the population of volumes is normally distributed.

(a) The company wants to estimate the mean volume of water the machine is putting in the bottles within 1 milliliter.  Determine the minimum sample size required to construct a 95% confidence interval for the population mean.  Assume the population standard deviation is 3 milliliters.
(b) Repeat part (a) using an error tolerance of 2 milliliters.  Which error tolerance requires a larger sample size?  Explain.

1. Find the standard normal distribution show on the right, find the probability of z occurring in the indicated region.
1. Assume the random variable x is normally distributed with mean = 50 and standard deviation = 7. P (X>35)

21.In a survey of 3068 adults, 1462 say they have started paying bills online in the last year.  Construct a 99% confidence interval for the population proportion.  Interpret the results.  Choose the correct answer below…

1. Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the try closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. 0.051.

1. In a survey of 640 male ages 18-64, 392 say they have gone to the dentist in the past year. Construct a 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval is 0.580, 0.644
The 95% confidence interval is 0.575, 0650
With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

1. Find the critical value Tc for the confidence level c = 0.80 and sample size n = 14.

Tc = 1.350

1. Assume the random variable x is normally distributed with mean u = 50 and standard deviation = 7. P ( X > 38)
23. For the standard normal distribution shown on the right, find the probability in the indicated region.

23.The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 206 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter.
A) what % of the men have a total cholesterol level less than 240 milligrams per deciliter of blood?
B) if 240 men in the 35-44 age group are randomly selected, about how many would you expect to have total cholesterol level greater than 252 milligrams per deciliter of blood?

MATH 221 Homework Week 1

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1  Determine whether the data set is a population or a sample. Explain your reasoning.

The age of each resident in an apartment building.

1  Determine whether the data set is a population or a sample. Explain your reasoning.

The salary of each baseball player in a league

1. Determine whether the data set is a population or a sample. The number of restaurants in each city in a state.

2  Determine whether the underlined value is a parameter or a statistic.

The average age of men who have walked on the moon was 39 years, 11 months, 15 days.

Is the value a parameter or a statistic?

2  Determine whether the data set is a population or a sample.  Explain your reasoning.

The number of pets for 20 households in a town of 300 households.

1. Determine whether the data is a population or sample. The age of one person per row in a cinema.

3  Determine whether the given value is a statistic or a parameter.

In a study of all 3336 professors at a college, it is found that 55% own a vehicle.

3  Determine whether the underlined value is a parameter or a statistic.

In a national survey of high school students (grades 9-12), 25% or respondents reported that someone had offered, sold, or given them an illegal drug on school property.

1. Determine whether the underlined value is a parameter or a statistic.
The average age of men who have walked on the moon was 39 years, 11 months, 15 days.

4  Determine whether the given value is a statistic or a parameter.

In a study of all 4901 professors at a college, it is found that 35% own a television.

4  Determine whether the given value is a parameter or a statistic.

In a study of all 1290 employees at a college, it is found that 40% own a computer.

1. Determine whether the given value is a statistic or a parameter.
A sample of professors is selected and it is found that 65% own a television.
5  Determine whether the variable is qualitative or quantitative.

Favorite film Is the variable qualitative or quantitative?

5  Determine whether the given value is a statistic or a parameter.

A sample of employees is selected and it is found that 45% own a vehicle.

1. Determine whether the given value is a statistic or a parameter.
A sample of seniors is selected and it is found that 65% own a computer.

6  Determine whether the variable is qualitative or quantitative.

Hair color Is the variable qualitative or quantitative?

6  Determine whether the variable is qualitative or quantitative.

Favorite sport Is the variable qualitative or quantitative?

1. Determine whether the variable is qualitative or quantitative
Favorite Film

7  The regions of a country with the six highest per capital incomes last year are shown below.

1. Southeast Western  3 Eastern  4 Northeast  5 Southeast   6 Northern

Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement.  What is the data set’s level of measurement?

1.  Ratio B.  Ordinal C.  Interval  D. Nominal

7  Determine whether the variable is qualitative or quantitative.

Car license  Is the variable Quantitative?

7.Determine whether the variable is qualitative or quantitative
Gallons of water in a swimming pool

8  Which method of data collection should be used to collect data for the following study.  The average age of the 105 residents of a retirement community.

8  The region representing the top salesperson is a corporation for the past six years is shown below.

Northern          Northern          Eastern                        Southeast        Eastern                        Northern

Determine whether the data are qualitative or quantitative and identify the data set’s level of measurement.  Are the data qualitative or quantitative?  What is the data set’s level of measurement?

1. The region of a country with the longest life expectancy for the past six years is shown below.

Western, Southeast, Southwest, Northeast, Northeast, Southeast,

9  Decide which method of data collection you would use to collect data for the study.

A study of the effect on the taste of a popular soda made with a caffeine substitute.

9  Which method of data collection should be used to collect data for the following study.

The average weight of 188 students in a high school.

1. Which method of data collection should be used to collect data for the following study.
The average age of 124 residents of a retirement community

10  Microsoft wants to administer a satisfaction survey to its customers. Using their customer database, the company randomly selects 60 customers and asks them about their level of satisfaction with the company.  What type of sampling is used?

10 Decide which method of data collection you would use to collect data for the study.

A study of the effect on the human digestive system of a snack food made with a sugar substitute.

1. Decide which method of data collection you would use to collect data for the study.
A study of the effect on human digestive system of a snack food made with a fat substitute.
11  A newspaper asks its readers to call in their opinion regarding the number of books they have read this month. What type sampling is used?

11  General Motors wants to administer a satisfaction survey to its current customers.  Using their customer database, the company randomly selects 80 customers and asks them about their level of satisfaction with the company.  What type of sampling is used?

12  Determine whether you would take a census or a sampling to collect data for the study described below.

The most popular chain restaurant among the 60,000 employees of a company.  Would you take a census or use a sampling?

1. Sony wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 50 customers and asks them about what their level of satisfaction with the company.
12  A magazine asks its readers to call in their opinion regarding the quality of the articles. What type of sampling is used?
2. A television station asks its viewers to call in their opinion regarding the desirability of programs in high definition TV.

13  Math the plot with a possible description of the sample.

1.  Top speeds (in miles per hour) of a sample of sports cars
2.  Time (in minutes) it takes a sample of employees to drive to work
3.  Grade point averages of a sample of students with finance majors
4.  Ages (in years) of a sample of residents of a retirement home

13  Determine whether you would take a census or use a sampling to collect data for the study described below.

The most popular house color among the 40,000 employees of a company.  Would you take a census or use a sampling?

1. Determine whether you would take a census or use a sampling to collect data for the study described below. The most popular chain restaurant among the 35 employees of a company.

14  Use a stem-and-leaf plot to display the data. The data represent the heights of eruptions by geyser.  What can you conclude about the data?

108                  90                    110                  150
140                  120                  100                  130
110                  100                  118                  106
98                    102                  105                  120
111                  130                  96                    124

Choose the correct stem-and-leaf plot. (Key: 15 ǀ 5 = 155)

What can you conclude about the data?

14  Match the plot with a possible description of the sample.

1.  Fastest serve (in miles per hour) of a sample of top tennis players
2.  Grade point averages of a sample of students with finance major
3.  Time (in minutes) it takes a sample of employees to drive to work
4.  Ages (in years) of a sample of residents of a retirement home

14.Match the plot with a possible description of the sample.

15  Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

1.  Skewed right
2.  Skewed left
3.  Symmetric
4.  Uniform
5.  None of these

15  Use a stem-and-leaf plot to display the data.  The data represent the heights of eruptions by a geyser.  What can you conclude about the data?

106                  90                    110                  150
140                  120                  100                  130
110                  101                  115                  100
99                    107                  103                  120
115                  130                  95                    121

What can you conclude about the data?

16  The maximum number of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data.

5 7 8 8 5 6 4 4 4 4 4 4 5

Find the mean.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The mean is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a mean.

Find the median.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a median.

Find the mode.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a mode.

16  Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of those.

1.  Skewed right
2.  Skewed left
3.  Symmetric
4.  Uniform
5.  None of these

Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.

17  Find the range, mean, variance, and standard deviation of the sample data set.
14 12 13 8 20 7 18 16 15

The range is

17 The maximum number of seats in a sample of 13 sport utility vehicles are listed below.  Find the mean, median, and mode of the data.
8 10 11 11 8 7 7 7 9 7 7 7 8

Find the mean.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The mean is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a mean.

Find the median.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The median is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a median

Find the mode.  Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

1.  The mode is

(Type the integer or decimal rounded to the nearest tenth as needed)

1.  The data does not have a mode
2. The maximum # of seats in a sample of 13 sport utility vehicles are listed below. Find the mean, median, and mode of the data. 8 8 11 11 8 7 7 7 9 7 7 7 10

Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

18  The ages of 10 brides at their first marriage are given below.

35.9  32.6  28.7  37.7  44.7  31.3  29.5  23.2  22.4  33.6

(a) Find the range of the data set.
Range = (round to the nearest tenth as needed)
(b) Change 44.7 to 61.3 and find the range of the new data set.
Range = 38.9 (round to the nearest tenth as needed)

1.  Changing the maximum value of the data set does not affect the range
2.  Changing the minimum value of the data set does not affect the range
3.  Changing the minimum value of the data set greatly affects the range
4.  Changing the maximum value of the data set greatly affects the range

18  Find the range, mean, variance, and standard deviation of the sample data set.
10 14 13 5 19 11 18 12 9

The range is

1. Find the range, mean, variance, and standard deviation of the sample data set.
8 15 14 17 9 7 13 11 20

19  Heights of men on a baseball team have a bell-shaped distribution with a mean of 185 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

1.  173 cm and 197 cm
2.  167 cm and 203 cm

A % of the men are between 173 cm and 197 cm
B % of the men are between 167 cm and 203 cm (Do not round)

19.The ages of 10 brides at their first marriage are given below.
24.4 31.8 35.8 32.5 44.2 24.5 26.2 24.6 22.5 27.2

20  The mean value of land and buildings per acre from a sample of farms is \$1400, with a standard deviation of \$100. The data set has a bell-shaped distribution.  Assume the number of farms in the sample is 70.

1.  Use the empirical rule to estimate the number of farms whose land and building values per acre are between \$1300 and \$1500.

farms (Round to the nearest whole number as needed)

1.  If 28 additional farms were sampled, about how many of these additional farms would you expect to have land and building value between \$1300 per acre and \$1500 per acre?
2. Heights of men on a baseball team have a bell-shaped distribution with a mean of 182 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?
A. 170 cm and 194 cm
B. 176 cm and 188 cm

21   Use the box-and-whisker plot to identify

(a)  The minimum entry
(b)  The maximum entry
(c)  The first quartile
(d)  The second quartile
(e)  The third quartile
(f)  The interquartile range

(a)  Min =
(b)  Max =
(c)  Q 1 =
(d)  Q 2 =
(e)  Q 3 =
(f)  IQR =

19  The ages of 10 brides at their first marriage are given below
22.6  23.7  35.6  39.2  44.7  29.6  30.8  31.7  24.5  28.2

(a) Find the range of the data set
Range =

(b) Change 44.7 to 68.3 and find the range of the new data set
Range =

1.  Changing the maximum value of the data set greatly affects the range
2.  Changing the minimum value of the data set greatly affects the range
3.  Changing the maximum value of the data set does not affect the range
4.  Changing the minimum value of the data set does not affect the range

20  Heights of men on a baseball team have a bell-shaped distribution with a mean of 172 cm and a standard deviation of 7 cm.  Using the empirical rule, what is the approximate percentage of the men between the following values?

1.  151 cm and 193 cm
2.  165 cm and 179 cm
3.  % of the men are between 151 cm and 193 cm (Do not round)
4.  % of the men are between 165 cm and 179 cm (Do not round)

20  The midpoints A, B, and C are marked on the histogram. Match them to the indicated scores.  Which scores, if any, would be considered unusual?

The point A corresponds with z = The point B corresponds with z =
The point C corresponds with z =
Which scores, if any, would be considered unusual?

1.  41
2.  -2.17
3.  0
4.  None

MATH 221 Homework Week 2

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1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
1. Discuss the difference between r and p

R represents the sample correlation coefficient.
P represents the population correlation coefficient

1. Discuss the difference between r and p.
2. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

A.  no linear correlation
B.  strong positive linear correlation
C.  strong negative linear correlation
D.  perfect negative linear correlation
E.  perfect positive linear correlation

3   The scatter plot of a paired data set is shown.  Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

1. The scatter plot of a paired data set is shown. Determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

4  Identify the explanatory variable and the response variable.

A golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

4  Identify the explanatory variable and the response variable.

A teacher wants to determine if the amount of textbook used by her students can be used to predict the students’ test scores

4.Identify the explanatory variable and the response variable.
a golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

5   Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

6  Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

1.  Prediction values are meaningful for all x-values that are realistic in the context of the original data set.
2.  Prediction values are meaningful for all x-values that are not included in the original data set.
3.  Prediction values are meaningful for all x-values in (or close to) the range of the original data.

5.Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

7  Match this description with a description below.

The y-value of a data point corresponding to

8  Match this description with a description below.

The y-value for a point on the regression line corresponding to

1. Match this description with a description below.
the y-value of a data point corresponding to x

9  Match the description below with its symbol(s).

The mean of the y-values

Select the correct choice below.

10  Match the regression equation  with the appropriate graph.

10  Match the regression equation with the appropriate graph.

11

1. Match the regression equation y = 1.662x + 83.34 with the appropriate graph.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R= -0.312

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.  About the unexplained variation?
% of the variation is unexplained and is due to other factors or to sampling error.  (Round to three decimal places as needed)

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R= -0.324

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.  About the unexplained variation?
% of the variation is unexplained and is due to other factors or to sampling error.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.481

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.

12  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.224

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.

12  The equation used to predict college GPA (range 0-4.0) is

is high school GPA (range 0-4.0) and x2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.5 and college board score of 400.

The predicted college GOA for a high school GPA of 3.5 and college board of 400 is.  (Round to the nearest tenth as needed).

1. Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? R = 0.862

13  Use the value of the linear correlation coefficient to calculate the coefficient of determination.  What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?

R = 0.909

Calculate the coefficient of determination

What does this tell you about the explained variation of the data about the regression line?
% of the variation can be explained by the regression line.
% of the variation is unexplained and is due to other factors or to sampling error.  (Round to three decimal places as needed)

13  The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is the female athlete’s height (in inches) and x2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 64 inches tall and has 17% body fat.

The predicted total body weight for a female athlete who is 64 inches tall and has 17% body fat is pounds.

13.Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the about the regression line? About the unexplained variation? R = 0.592

14  The equation used to predict college GPA (range 0-4.0) is

high school GPA (range 0-4.0) and X2 is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of 3.2 and a college board score of 500.

The predicted college GPA for a high school GPA of 3.2 and college board score of 500 is.

14.The equation used to predict college GPA (range 0-4.0) is y = 0.21 + 0.52x + 0.002x, where x is high school GPA (range 0-4.0) and x is college board score (range 200-800). Use the multiple regression equation to predict college gpa for a high school gpa of 3.2 and a college board score of 600.

15  The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is  the female athlete’s height (in inches) and X2 is the female athlete’s percent body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 67 inches tall and has 24% body fat.

The predicted total body weight for a female athlete who is 67 inches tall and has 24% body fat is pounds.

15.The equation used to predict the total body weight of a female athlete at a certain school is y = -112 + 3.29x + 1.64x, where x is the female athlete’s height and x is the females athlete’s % body fat. Use the multiple regression equation to predict the total body weight for a female athlete who is 63 inches tall and has 19% body fat.

MATH 221 Homework Week 3

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1  The access code for a car’s security system consist of four digits. The first digit cannot be zero and the last digit must be odd.  How many different codes are available?

1  The access code for a car’s security system consist of four digits. The first digit cannot be 6 and the last digit must be even or zero.  How many different codes are available?

1.The access code for a car’s security system consists of four digits. The first digit cannot be 1 and must e even or 0. How many different codes are there?

2  A probability experiment consists of rolling a 6-sided die. Find the probability of the event below:

Rolling a number is less than 5

2  A probability experiment consists of rolling a 6-sided die. Find the probability of the event below:

Rolling a number is less than 4

1. A probability experiment consists of rolling a 6-sided die. Find the probability of rolling a number less than 4.

3  Use the frequency distribution, which shows the responses of a survey of college students when asked, “How often do you wear a seat belt when riding in a car driven by someone else?” Find the following probabilities of responses of college students from the survey chosen at random.

Use the frequency distribution, which shows the responses of a survey of college students when asked, “how often do you wear a seat belt when riding in a car driven by someone else? Find the following probability of responses of college students from the survey chosen at random.

4  Determine whether the events E and F are independent or dependent. Justify your answer.

1.  E: A person having an at-fault accident.

F: The same person being prone to road rage.

1.  E and F are dependent because having an at-fault accident has no effect on the probability of a person being prone to road rage.
2.  E and F are dependent because being prone to road rage can affect the probability of a person having an at-fault accident.
3.  E and F are independent because having an at-fault accident has no effect on the probability of a person being prone to road rage.
4.  E and F are independent because being prone to road rage has no effect on the probability of a person having an at-fault accident.
5.  E: A randomly selected person accidentally killing a spider.

F: Another randomly selected person accidentally swallowing a spider.

1.  E can affect the probability of F, even if the two people are randomly selected, so the events are dependent.
2.  E can affect the probability of F because the people were randomly selected, so the events are dependent.
3.  E cannot affect F and vice versa because the people were randomly selected, so the events are independent.
4.  E cannot affect F because “person 1 accidentally killing a spider” could never occur, so the events are neither dependent nor independent.
5.  E: The consumer demand for synthetic diamonds.

F: The amount of research funding for diamond synthesis.

1.  The consumer demand for synthetic diamonds could not affect the amount of research funding for diamond synthesis, so E and F are independent.
2.  The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis, so E and F are dependent.
3.  The amount of research funding for diamond synthesis could affect the consumer demand for synthetic diamonds, so E and F are dependent.
4.  E: The unusually foggy weather in London on May 8

F: The number of car accidents in London on May 8

1.  The unusually foggy weather in London on May 8 could not affect the number of car accidents in London on May 8, so E and F are independent.
2.  The number of car accidents in London on May 8 could affect the unusually foggy weather in London on May 8, so E and F are dependent
3.  The unusually foggy weather in London on May 8 could affect the number of car accidents in London on May 8, so E and F are dependent
4. Determine whether the events E and F are independent or dependent. Justify your answer.
(a)
E: A person having an at-fault accident
F: The same person being prone to road rage

(b)
E: A randomly selected person accidentally killing a spider.
F: Another random person swallowing a spider

(c)
E: The consumer demand for synthetic diamonds
F: The amount of research funding for diamond synthesis

5  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

 Summer Vacation This Year Yes                 No                  Total Own a             Yes                  46                    11                    57 Computer        No                   56                    34                    90 Total                                        102                  45                    147

a.  Find the probability that a randomly selected family is not taking a summer vacation this year.
The probability is (Round to the nearest thousandth as needed.)
b.  Find the probability that a randomly selected family owns a computer.
The probability is (Round to the nearest thousandth as needed.)
c.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.
The probability is (Round to the nearest thousandth as needed.)
d.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.
The probability is (Round to the nearest thousandth as needed.)
e.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?

6  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

 Summer Vacation This Year Yes                  No                   Total Own a             Yes                  47                    11                    58 Computer        No                   56                    33                    89 Total                                        103                  44                    147
1.  Find the probability that a randomly selected family is not taking a summer vacation this year.

The probability is

1.  Find the probability that a randomly selected family owns a computer.

The probability is

1.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.

The probability is

1.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.

The probability is (Round to the nearest thousandth as needed.)

1.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?
2. The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a summer vacation this year.(A) Find the probability that a random family is not taking a summer vacation this year.
(B) Find the probability that a random family owns a computer
(C) Find the probability that a random family is taking a vacation given that they own a computer
(D) Find the probability that a random family is taking a vacation and own a computer.
(E) Are the events of owning a computer and taking a vacation independent or dependent?6  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

 Summer Vacation This Year Yes                  No                   Total Own a             Yes                  47                    11                    58 Computer        No                   56                    33                    89 Total                                        103                  44                    147
1. a.  Find the probability that a randomly selected family is not taking a summer vacation this year.

The probability is

1.  Find the probability that a randomly selected family owns a computer.

The probability is

1.  Find the probability that a randomly selected family is taking a summer vacation this year given that they own a computer.

The probability is

1.  Find the probability that a randomly selected family is taking a summer vacation this year and owns a computer.

The probability is

1.  Are the events of owning a computer and taking a summer vacation this year independent or dependent events?

7  A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement.  Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory.

7  A distribution center receives shipments of a product from three different factories in the quantities of 50, 30, and 20. Three times a product is selected at random, each time without replacement.  Find the probability that (a) all three products came from the second factory and (b) none of the three products came from the second factory.

1.  The probability that all three products came from the second factory is
2.  The probability that none of the three products came from the second factory is

a.  The probability that all three products came from the second factory is
(Round to the nearest thousandth as needed.)
b.  The probability that none of the three products came from the second factory is
(Round to the nearest thousandth as needed.)

8  A standard deck of cards contains 52 cards. One card is selected from the deck.

a.  Compute the probability of randomly selecting a spade or heart
b.  Compute the probability of randomly selecting a spade or heart or diamond
c.  Compute the probability of randomly selecting a seven or club

a.  P(spade of heart)= (Type an integer or a simplified fraction.)

b.  P(spade or heart or diamond)= (Type an integer or a simplified fraction.)

c.  P(seven or club)= (Type an integer or a simplified fraction.)

8  A standard deck of cards contains 52 cards. One card is selected from the deck.

a.  Compute the probability of randomly selecting a three or eight
b.  Compute the probability of randomly selecting a three or eight of king
c.  Compute the probability of randomly selecting a queen or diamond

a.  P(spade of heart)= (Type an integer or a simplified fraction.)

b.  P(spade or heart or diamond)= (Type an integer or a simplified fraction.)

c.  P(seven or club)= (Type an integer or a simplified fraction.)

9  The percent distribution of live multiple-delivery births (three or more babies) in a particular year for a women 15 to 54 years old is shown in the pie chart. Find each probability.

10  The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random.  Complete parts (a) through (d).

Nursing majors                        Non-nursing majors                 Total

Males                                       92                                1019                            1111
Females                                   700                              1725                            2425
Total                                        792                              2744                            3536

1.  Find the probability that the student is male or a nursing major

P (being male or being nursing major) =

1.  Find the probability that the student is female or not a nursing major.

P( being female or not a nursing major) =

1.  Find the probability that the student is not female or a nursing major

P(not being female or being a nursing major) =

Are the events “being male” and “being a nursing major” mutually exclusive?

1.  No, because there are 92 males majoring in nursing
2.  No, because one can’t be male and a nursing major at the same time
3.  Yes, because one can’t be male and a nursing major at the same time
4.  Yes, because there are 97 males majoring in nursing

10  The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random.  Complete parts (a) through (d).

Nursing majors                        Non-nursing majors                 Total

Males                                       97                                1017                            1114
Females                                   700                              1727                            2427
Total                                        797                              2744                            3541

1.  Find the probability that the student is male or a nursing major

P (being male or being nursing major) =

1.  Find the probability that the student is female or not a nursing major.

P( being female or not a nursing major) =

1.  Find the probability that the student is not female or a nursing major

P(not being female or being a nursing major)

Are the events “being male” and “being a nursing major” mutually exclusive?

1.  No, because there are 97 males majoring in nursing
2.  No, because one can’t be male and a nursing major at the same time
3.  Yes, because one can’t be male and a nursing major at the same time
4.  Yes, because there are 97 males majoring in nursing
5. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there?

11   Outside a home, there is an 10-key keypad with letters A, B, C, D, E, F, G and H that can be used to open the garage if the correct ten-letter code is entered. Each key may be used only once.  How many codes are possible?

The number of possible codes is

1. Outside a home, there is a 4-key keypad with the letters a,b,c, and d that can open the garage if the correct 4 letter code is entered. Each key may only be used once, how many possible codes are there?

12  How many different 10-letter words (real or imaginary) can be formed from the following letters?
Z, V, U, G, X, V, H, G, D

ten-letter words (real or imaginary) can be formed with the given letters.

12  How many different 10-letter words (real or imaginary) can be formed from the following letters?
K, I, B, W, E, Z, I, O, R, Z

ten-letter words (real or imaginary) can be formed with the given letters.

1. A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those 2 horses finish first and second (regardless of order)

13  A horse race has 13 entries and one person owns 2 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

The probability that those two horses finish first, second, third, and fourth is

13  A horse race has 13 entries and one person owns 4 of those horses. Assuming that there are no ties, what is the probability that those four horses finish first, second, third, and fourth (regardless of order)?

The probability that those four horses finish first, second, third, and fourth is

1. Determine the required value of the missing probability to make the distribution a discrete probability distribution.

14  Determine the required value of the missing probability to make the distribution a discrete probability distribution.

X         P(x)
3          0.19
4          ?
5          0.34
6          0.28

P() = (Type an integer or a decimal)

14  Determine the required value of the missing probability to make the distribution a discrete probability distribution.

X         P(x)
3          0.16
4          ?
5          0.38
6          0.17

P() = (Type an integer or a decimal)

1. A frequency distribution is shown below. Complete a – e.

X         P(x)
0          0.635
1          0.228
2          0.089
3          0.024
4          0.014
5          0.009

15.

Students in a class take a quiz with 8 questions. The number x of questions answered correctly can be approximated by the following probability distribution. Complete a – e.

15  A frequency distribution is shown below. Complete parts (a) through (e).

Dogs                0          1          2          3          4          5
Household       1324    436      162      46        27        15

1.  Use the frequency distribution to construct a probability distribution.

X         P(x)
0
1
2
3
4
5

1.  Find the mean of the probability distribution

µ = (Round to the nearest thousandth as needed.)

1.  Find the variance of the probability distribution

= (Round to the nearest tenth as needed)

1.  Find the standard deviation of the probability distribution
• = (Round to the nearest tenth as needed)
• e.  Interpret the results in the context of the real-life situation.
• A.  A household on average has 0.5 dog with a standard deviation of 0.9 dog.
1. B.  A household on average has 0.5 dog with a standard deviation of 15 dog.
2. C.  A household on average has 0.9 dog with a standard deviation of 0.5 dog.
3. D.  A household on average has 0.9 dog with a standard deviation of 0.9 dog.

17  Students in a class take a quiz with eight questions. The number x of questions answered correctly can be approximated by the following probability distribution.  Complete parts (a) through (e).

X         0          1          2          3          4          5          6          7          8

P(x)     0.02     0.02     0.06     0.06     0.14     0.24     0.27     0.12     0.07

(a)  Use the probability distribution to find the mean of the probability distribution
µ =
(b)  Use the probability distribution to find the variance of the probability distribution
=
(c)  Use the probability distribution to find the standard deviation of the probability distribution
(d)  Use the probability distribution to find the expected value of the probability distribution

Interpret the results

1.  The expected number of questions answered correctly is 5.1 with a standard deviation of 1.8 questions.
2.  The expected number of questions answered correctly is 1.8 with a standard deviation of 5.1 questions.
3.  The expected number of questions answered correctly is 5.1 with a standard deviation of 0.02 questions.
4.  The expected number of questions answered correctly is 3.1 with a standard deviation of 1.8 questions.

MATH 221 Homework Week 4

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1. The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram

a.  Choose the correct answer below. Use histogram

A.  X = 0, x = 1, x = 2, x = 3, and x = 4
B.  X = 3 and x = 4
C.  X = 0 and x = 1
D.  There are no unusual values of x in the histogram

b.  X = 7

A.  X = 0, x = 1, x = 2, x = 3, and x = 4
B.  X = 0 and x = 1
C.  X = 0 and x = 1
D.  There are no unusual values of x in the histogram

2  The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram.

(a)  N = 4
(b)  N = 8

a.  Choose the correct answer below. Use histogram (a).

A.  X = 4
B.  X = 0, x =7, and x = 8
C.  X = 2
D.  There are no unusual values of x in the histogram

b.  Choose the correct answer below. Use the histogram (b)

A.  X =0, x =7, and x = 8
B.  X = 4
C.  X = 4
D.  There are no unusual values of x in the histogram

2  The histograms each represents part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n.  Identify the unusual values of x in each histogram.

(a)  N = 4
(b)  N = 8

a. Choose the correct answer below. Use histogram (a)

A. X = 4
B. X = 0, x =7, and x = 8
C. X = 2
D. There are no unusual values of x in the histogram

b.Choose the correct answer below. Use the histogram (b)

A. X =0, x =7, and x = 8
B. X = 4
C. X = 4
D. There are no unusual values of x in the histogram

2. About 30% of babies born with a certain ailment recover fully. A hospital is caring for 7 babies born with this ailment. The random variable represents the # of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specific the values of n, p , and q, and list the values of random variable x.

3  About 80% of babies born with a certain ailment recover fully. A hospital is caring for five babies born with this ailment.  The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

Yes
No

What is a success in this experiment?

Baby doesn’t recover
Baby recovers
This is not a binomial experiment
Specify the value of n.  Select the correct choice below and fill in any answer boxes in your choice.
N =
This is not a binomial experiment
Specify the value of p.  Select the correct choice below and fill in any answer boxes in your choice.
P =
This is not a binomial experiment
Specify the value of q.  Select the correct choice below and fill in any answer boxes in your choice.
Q =
This is not a binomial experiment

List the possible values of the random variable x.

X = 1, 2, 3,…, 5
X = 0, 1, 2, ….4
X = 0, 1, 2, …5

This is not a binomial experiment

3  About 70% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment.  The random variable represents the number of babies that recover fully.  Decide whether the experiment is a binomial experiment.  If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x.

Is the experiment a binomial experiment?

A.  No
B.  Yes

What is a success in this experiment?

A.  Baby recovers
B.  Baby doesn’t recover
C.  This is not a binomial experiment

Specify the value of n.  Select the correct choice below and fill in any answer boxes in your choice.

A.  N =
B.  This is not a binomial experiment

Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice.
p=

This is not a binomial experiment

Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice.
q =

This is not a binomial experiment

List the possible values of the random variable x.

A.  X = 0, 1, 2,…,5
B.  X = 0, 1, 2,…6
C.  X = 1, 2, 3,…6
D.  This is not a binomial experiment

1. Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
n = 125, p = 0.81

4  Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

N = 129, p = 0.43

The mean, µ is (Round to the nearest tenth as needed.)
The variance,  is (Round to the nearest tenth as needed.)

The standard deviation,  is (Round to the nearest tenth as needed.)

1. 56% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the # who consider themselves baseball fans is (a) 8, (b) at least 8, (c) less than 8.

5  Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.

N = 121, p = 0.27
The mean, µ is (Round to the nearest tenth as needed.)
The variance,  is (Round to the nearest tenth as needed.)
The standard deviation,  is (Round to the nearest tenth as needed.)

1. 45% of households say they would feel secure if they had at least \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings. Find the probability that the # that they say would feel secure is (a) exactly 5, (b) more than 5 or (c) at most 5.

6  48% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan.  Find the probability that the number who consider themselves baseball fans is (a) exactly eight, (b) at least eight, and (c) less than eight.  If convenient, use technology to find the probabilities.

a.  P(8) = (Round to the nearest thousandth as needed)
b.  P(x≥8) = (Round to the nearest thousandth as needed)
c.  P(x<8) = (Round to the nearest thousandth as needed)

1. 43% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask them to name his or her favorite nut. Find the probability that the # who say cashews are their favorite nut is (a) exactly 4, (b) at least 4, and (c) at most 2.

7  Seventy-five percent of households say they would feel secure if they had \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

a.  Find the probability that the number that say they would feel secure is exactly five.
P(5) = (Round to three decimal places as needed)
b.  Find the probability that the number sat they would feel secure is more than five.
P(x>5) = (Round to three decimal places as needed)
c.  Find the probability that the number that say they would feel secure is at most five.
P(x≤5) = (Round to three decimal places as needed)

1. 24% of college students say they use credit cards. You randomly select 10 students and ask them why they use credit cards because of the rewards program. (a) Exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive.

8  Sixty-five percent of households say they would feel secure if they had \$50,000 in savings. You randomly select 8 households and ask them if they would feel secure if they had \$50,000 in savings.  Find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five.

a.  Find the probability that the number that say they would feel secure is exactly five.
P(5) = (Round to three decimal places as needed)
b.  Find the probability that the number sat they would feel secure is more than five.
P(x>5) = (Round to three decimal places as needed)
c.  Find the probability that the number that say they would feel secure is at most five.
P(x≤5) = (Round to three decimal places as needed)

1. 34% of women consider themselves of baseball. You randomly select 6 women and ask each if she considers herself a fan of baseball.

X         p(x)
0          0.083
1          0.255
2          0.329
3          0.226
4          0.087
5          0.018
6          0.002

9  34% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.  Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.

a.  P(3) = (Round to the nearest thousandth as needed.)
b.  P(x > 4) = (Round to the nearest thousandth as needed.)
c.  P(x < 2) = (Round to the nearest thousandth as needed)

1. Given that x has a Poisson distribution with mean = 4, what is the probability that x = 2?

10   33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut.  Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities

a.  P(3) = (Round to the nearest thousandth as needed.)
b.  P(x > 4) = (Round to the nearest thousandth as needed.)
c.  P(x < 2) = (Round to the nearest thousandth as needed)

1. Given that x has a Poisson distribution with mean = 1.9, what is the probability that x = 3?

11.  21% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the # of college students who say they use credit cards because of the rewards program is (a) exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive. If convenient, use technology to find the probabilities.

a.  P(2) = (Round to the nearest thousandth as needed.)
b.  P(X > 2) = (Round to the nearest thousandth as needed.)
c.  P(X < 5) = (Round to the nearest thousandth as needed.)

1. Decide whether binomial, geometric, or Poisson applies to this question.
In a certain city, the mean # of days with 0.01 inch or more precipitation for May is 13.What is the probability that the city has 21 days with 0.01 inch or more next may?

12.  38% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the # of college students who say they use credit cards because of the rewards program is (a) exactly 2, (b) more than 2, and (c) between 2 and 5 inclusive. If convenient, use technology to find the probabilities.

a.  P(2) = (Round to the nearest thousandth as needed.)
b.  P(X > 2) = (Round to the nearest thousandth as needed.)
c.  P(X < 5) = (Round to the nearest thousandth as needed.)

1. Decide whether binomial, geometric, or Poisson applies to this question.
The mean # of oil tankers at a port city is 6 per day. The port has facilities to handle up to 9 oil tankers in a day. What is the probability that too many tankers will arrive on a given day?

13.  36% of women consider themselves fan of professional baseball. You randomly select 6 women and ask each if they consider themselves a fan of professional baseball.

a.  Construct a binomial distribution using n = 6 and p = 0.36

X                     P(x)
0
1

b.  Choose the correct histogram for this distribution below.

c.  Describe the shape of the histogram

A.  Skewed right
B.  Skewed left
C.  Symmetrical
D.  None of these

d.  Find the mean of the binomial distribution

µ = (round to the nearest 10th as needed)
( e ) find the variance of the binomial distribution.
= (round to the nearest 10th as needed.)
( f ) Find the standard deviation of the binomial distribution.
= (round to the nearest 10th as needed)
( g ) Interpret the results in the context of the real-life situation. What values of the random variable would you consider unusual? Explain your reasoning.

On average, out of 6 women consider themselves baseball fans, with a standard deviation of  women. The values x=6 and x= would be unusual because their probabilities are less than 0.05.

1. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.18. find the probability that you (a) make your first sale on the 5th call, (b) make your sale on the 1st, 2nd, or 3rd call, and (C) do not make the sale on the first 3 calls.

14.  38% of women consider themselves fan of professional baseball. You randomly select 6 women and ask each if they consider themselves a fan of professional baseball

(a) Construct a binomial distribution using n = 6 and p = 0.38

X                     P(x
0
1
2
3
4
5
6

(b)  Choose the correct histogram for this distribution below.

(c).  Describe the shape of the histogram

A.  Skewed right
B.  Skewed left
C.  Symmetrical
D.  None of these

(d)  Find the mean of the binomial distribution
µ = (round to the nearest 10th as needed)
( e ) find the variance of the binomial distribution.
= (round to the nearest 10th as needed.)
( f ) Find the standard deviation of the binomial distribution.
=  (round to the nearest 10th as needed)
( g ) Interpret the results in the context of the real-life situation. What values of the random variable would you consider unusual? Explain your reasoning.

On average, out of 6 women consider themselves baseball fans, with a standard deviation of women. The values x= and x= would be unusual because their probabilities are less than .

1. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A newspaper finds that the mean # of typographical errors per page is 7. Find the probability that (a) exactly 6 typos are found on a page, (b) at most 6 are found on a page, and (c) more than 6 are found on a page.
2. Find the indicated probabilities using geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A major hurricane is a hurricane with wind speeds of 111 miles per hour or more. During the last century, the mean # of major hurricanes to strike was about 0.62. find the probability that in a given year is (a) exactly one hurricane, (b) at most one, and (c) more than one.

15.  Given that x has a Poisson distribution with µ = 3, what is the probability that x = 5?

P(5) ≈ (round to 4 decimal places as needed.)

1. Given that x has a Poisson distribution with µ = 4, what is the probability that x = 3?

P(3) ≈ (round to 4 decimal places as needed.)

1. Given that x has a Poisson distribution with µ = 1.6, what is the probability that x = 5?

P(5) ≈ (round to 4 decimal places as needed.)

1. Given that x has a Poisson distribution with µ = 0.5, what is the probability that x = 0?

P(0) ≈ (round to 4 decimal places as needed.)

1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need 2 answer the question.

Given: of students ages 16 to 18 with A or B averages who plan to attend college after graduation, 60% cheated to get higher grades. 10 randomly chosen students with A or B to attend college after graduation were asked if they cheated to get higher grades. Question: what is the probability that exactly two students answered no?

A.  Poisson distribution
B.  Binomial distribution
C.  Geometric distribution

1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need 2 answer the question. Instead, justify your choice.
Question: what is the probability that t00 many tankers will arrive on a given day?

A. Binomial.  You are interested in counting the number of successes out of n trials.
B. Poisson.  You are interested in counting the number of occurrences that take place within a given unit of time.
C.  Geometric.  You are interested in counting the number of trials until the first success.

1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need to answer the question.

Given: Of students ages 16 to 18 with A or B averages who plan to attend college after graduation, 65% cheated to get higher grades.  Ten randomly chosen students with A or B attend college after graduation were asked if the cheated to get higher grades.  Question: What is the probability that exactly two students answered no?

What type of distribution applies to the given question?

A.  Binomial distribution
B,  Geometric distribution
C.  Poisson distribution

1. Decide which probability distribution – binomial, geometric, or Poisson – applies to the question. You do not need to answer the question.  Instead, justify your choice.

Given: The mean number of oil tankers at a port city is 12 per day.  The port has facilities to handle up to 18 oil tankers in a day.

Choose the correct probability distribution below.

A.  Poisson.  You are interested in counting the number of occurrences that take place within a given unit of time.
B.  Binomial.  You are interested in counting the number of successes out of n trials.
C.  Geometric.  You are interested in counting the number of trials until the first success.

1. Find the indicated probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.14. Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the 1st, 2nd, or 3rd call, and (c) do not make a sale on the first 3 calls.
(a) P(make your first sale on the fifth call) =
(Round to three decimal places as needed.)
(b) P(make your sale on the first, second, or third call) =
(Round to three decimal places as needed.)
(c) P(do not make a sale on the first three calls) =
(Round to three decimal places as needed.)

Which of the events are unusual?  Select all that apply.

A.  The event in part (a), “make your first sale on the fifth call”, is unusual
B. The event in part (b), “make you sale on the first, second, or third call”, is unusualC.
C.  The event in part (c), “do not make a sale on the first three calls”, is unusual
D.  None of the events are unusual

1. Find the indicted probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.
A newspaper finds the mean number of typographical errors per page is four. Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typo errors are found on a page.
(a) P(exactly five typo errors are found on a page) =
(Round to four decimal places as needed.)
2. (b)P(at most five typographical errors are found on a page) =

(Round to four decimal places as needed.)
(c) P(more than five typo errors are found on a page) =
(Round to four decimal places as needed)

Which of the events are unusual?  Select all that apply.

A.  The event in part (a) is unusual.
B.  The event in part (b) is unusual.
C.  The event in part (c) is unusual.
D.  None of the events are unusual

1. Find the indicted probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.

A major hurricane is a hurricane with winds of 111 mph or greater. During the lsat century, the mean # of major hurricanes to strike a certain country’s mainland per year was about 0.46. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.
(a) P(exactly one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)
(b) P(at most one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)
(c) P(more than one major hurricane will strike the mainland) =
(Round to three decimal places as needed.)

Which of the events are unusual?  Select all that apply.

A.  The event in part (a) is unusual.
B.  The event in part (b) is unusual.
C.  The event in part (c) is unusual.
D.  None of the events are unusual

MATH 221 Homework Week 5

https://www.hiqualitytutorials.com/product/math-221-homework-week-5-statistics-for-decision/

1 A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates a normal distribution could be used a model for the variable.

A.  The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.
B.  The histogram is bell-shaped, so a normal distribution could be used as a model for the variable.
C.  The histogram is not bell-shaped, so a normal distribution could be used as a model for the variable.
D.  The histogram is bell-shaped, so a normal distribution could not be used as a model for the variable.

1  A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates a normal distribution could be used a model for the variable.

1.

A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

A.  The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.
B.  The histogram is bell-shaped, so a normal distribution could be used as a model for the variable.
C.  The histogram is not bell-shaped, so a normal distribution could be used as a model for the variable.
D.  The histogram is bell-shaped, so a normal distribution could not be used as a model for the variable.

2 Find the area of the shaded region. The graph depicts  the standard normal distribution with mean 0 and standard deviation 1.

The area of the shaded region is
(round to 4 decimal places as needed.)

2.

Find the area of the shaded region.

F  Find the area of the indicated region under the standard normal curve

The area between z = 0 and z = 1 under the standard normal curve is
(round to 4 decimal places as needed.)

3  Find the area of the indicated region under the standard normal curve.

The area between z  = 0 and z = 1.3 under the standard normal curve is
(round to 4 decimal places as needed.)

4  Find the indicated area under the standard normal curve.
To the left of z =

The area to the left of z = -0.28 under the standard normal curve is
(round to 4 decimal places as needed.)
4  Find the indicated area under the standard normal curve.
To the left of z =
The area to the left of z = – 0.28 under the standard normal curve is
round to four decimal places as needed.

1. Find the area under the standard normal curve. To the left of z = 2.26

5 Find the indicated area under the normal curve.
between z = -1.08 and z = 1.08
The area between z= -1.08 and z = 1.08 under the standard normal curve is
(round to 4 decimal places as needed.)

1. Find the indicated area under the standard normal curve. To the right of z = 0.42

6  Find the indicated area under the standard normal curve.
To the left of z =

The area to the left of z = under the standard curve is

6  Find the indicated area under the standard normal curve.

To the right of z =

The area to the right of z = under the standard normal curve is.

6  Find the indicated area under the standard normal curve.

Between z = and z =

The area between z = and z = under the standard normal curve is.

1. Find the indicated area under the standard normal curve. Between z = -0.48 and 0.48

7  Assume the random variable x is normally distributed with mean µ = 82 and standard deviation .  Find the indicated probability.

P(x<75)

P(x<75) = (Round to four decimal places as needed)

7  Assume random variable x is normally distributed with mean µ = 82 and standard deviation. Find the indicated probability.

P(x<78)
P(X<78) = (round to 4 decimal places as needed.

7  Assume random variable x is normally distributed with mean µ = 87 and standard deviation . Find the indicated probability.
P(75<x<84)
P(75<x<84) =
(round to 4 decimal places as needed.)

1. Assume the random variable x is normally distributed with a mean of 81 and standard deviation of 4. P(X<77)

8 Assume the random variable x is normally distributed with mean µ = 84 and standard deviation σ = 5.  Find the indicated probability.

P(68<x<74)
P(68<x74<) =

(Round to four decimal places as needed)

1. Assume the random variable x is distributed with mean of 90 and standard deviation of 5. P(63<x<88)

9  A survey was conducted to measure the height of men.  In the survey, respondents were grouped by age.  In the 20-29 age group, the heights were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.  A study participant is randomly selected.  Complete parts (a) through (c).

a.  Find the probability that his height is less than 67 inches.
The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed)
b.  Find the probability that his height is between 67 and 72 inches.
The probability that the study participant selected at random is between 67 inches and 72 inches tall is. (Round to four decimal places as needed)
c.  Find the probability that his height is more than 72 inches.
The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed)

9  A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (c).

A. find the probability that his height is less than 68 inches.
The probability that the student participant selected at random is less than 68 inches tall is (round to 4 decimal places as needed.)
B. find the probability that his height is between 68 and 71 inches
the probability that the student participant selected at random is between 68 and 71 inches tall is   (round to 4 decimal places as needed.)

C.  find the probability that his height is more than 71 inches.

The probability that the study participant selected at random is more than 71 inches tall is (round to 4 decimal places as needed).

1. A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.6 inches and a standard deviation of 3 inches. Complete parts a – c.
A) Find that probability that his height is less than 65 inches.
B) Find the probability that his height is between 65-70 inches.
C Find the probability that his height is more than 70 inches.

10 Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is 108.  Assume the variable x is normally distributed.
(a)  What percent of the SAT verbal scores are less than 650?
(b)  If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575?

a.  Approximately % of the SAT verbal scores are less than 650. (Round to two decimal places as need)
b.  You would expect that approximately SAT verbal scores would be greater than 575.  (Round to the nearest whole number as needed)

10 Use the normal distribution of Sat critical reading scores for which the mean is 514 and the standard deviation is 124. Assume the variable x is normally distributed.

1. Use the normal distribution of SAT crtical reading scores for which the mean is 502 and standard deviation is 119. Assume the variable x is normally distributed.
A) what % of the SAT scores are less than 675?
B) if 1000 SAT verbal scores are randomly selected, how many would be greater than 525?

A. what percent of the SAT verbal score is less than 500?
B. if 1000 sat scores are randomly selected, how many would be greater than 525?
A: %
B: greater than 525

11  Find the indicated z-score shown in the graph to the right.

The z-score is (Round to two decimal places as needed)

11 Find the indicated z-score shown in the graph to the right.

The z-score is

11  Find the indicated z-score shown in the graph to the right.

1. Find the z-score shown in the graph.

12 Find the indicated z-score shown in the graph to the right.

The z-score is
The z-score is (Round to two decimal places as needed)

12. Find the z-score shown in the graph.

13  Find the z-score that has 11.9% of the distribution’s area to its right.

The z-score is (Round to two decimal places as needed)

1. Find the z-score that has 27.1% of the distribution’s area to it’s right

13  Find the z-score that has 11.9% of the distribution’s area to its right.
The z-score is (Round to two decimal places as needed)

14  Find the z-scores for which 70% of the distribution’s area lies between –z and z.
The z-scores are

(Use a comma to separate answers as needed.  Round to two decimal places as needed)

14  Find the z-scores for which 98% of the distribution’s area lies between – z and z.
The z-scores are (Use a comma to separate answers as needed)

1. Find the z-score for which 70% of the distribution’s area is between –z and z.
2. In a survey of women in a certain country (ages 20-29), the mean height was 64.9 inches with a standard deviation of 2.86 inches. Answer the following questions:
A) what height represents the 85th percentile
B) what height represents the first quartile?

15 In a survey of women in a certain country (ages 20-29), the mean height was 66.5 inches with a standard deviation of 2.84 inches.  Answer the following questions about the specified normal distribution.

(a)  What height represents the 85th percentile?
(b)  What height represents the first quartile?

a.  The height the represents the 85th percentile is inches. (Round to two decimal places as needed)
b.  The height that represents the first quartile is inches. (Round to two decimal places as needed)

15  In a survey of women in a certain country (ages 20-29), the mean height was 65.9 inches with a standard deviation of 2.74 inches. Answer the following questions about the specified normal distribution.

(a)  What height represents the 95th percentile?
(b)  What height represents the first quartile?

a.  The height that represents the 95th percentile is inches. (Round to two decimal places as needed)
b.  The height that represents the first quartile is inches. (Round to two decimal places as needed)

16  The time spent (in days) waiting for a heart transplant in two states for patients with type A + blood can be approximately by a normal distribution, as shown in the graph.  Complete parts (a) and (b) below.

(a)  What is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times?
days (Round to two decimal places as needed)
(b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 29% of waiting times?

days. (Round to two decimal places as needed)

16  The time spent (in days) waiting for a heart transplant in two states for patients with type A + blood can be approximated by a normal distribution, as shown in the graph to the right. Complete parts (a) and (b) below.

(a)  What is the shortest time spent waiting for a heart that would still place a patient in the top 15% or waiting times?
days ( Round to two decimal places as needed)
(b) What is the longest time spent waiting for a heart that would still place a patient in the bottom 5% of waiting times?
days ( Round to two decimal places as needed)

16. The time spent waiting for a heart transplant in two states for patients with type A blood can be approximated by a normal distribution, as shown in the graph to the right.
A) what is the shortest time spent waiting for a heart that would still place a patient in the top 30% of waiting times?
B) what is the longest time spent waiting for a heart that would still place a patient in the bottom 1% of waiting times?

17   population has a mean µ = 86 and a standard deviation σ = 14.  Find the mean and standard deviation of a sampling distribution of a sampling distribution of sample means with sample size n = 49.

1. A population has a mean of 90 and standard deviation of 12. Find the mean and standard deviation of a sampling distribution of sample means with sample size n =36

18  The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population.  Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means.  Explain your reasoning.

1. The graph of waiting times at a red light is shown below on the left with its mean and standard deviation. Assume that a sample size of 100 is drawn from the population. Decide which of the graphs labeled a – c would most likely resemble the sampling distribution of the sample means.

18  The graph of the waiting time (in seconds) at a red light is shown below on the left with its mean and standard deviation.  Assume that a sample size of 100 is drawn from the population.  Decide which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means.  Explain your reasoning.

Graph ( ) most closely resembles the sampling distribution of the sample means, because

µ – =, σ – =, and the graph approximates a normal curve.

X              x

(Type an integer or a decimal)

19 A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 133 ounces and a standard deviation of 0.30 ounce.  You randomly select 50 cans and carefully measure the contents.  The sample mean of the cans is 132.9 ounces.  Does the machine need to be reset?  Explain your reasoning.

19  A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 132 ounces and a standard deviation of 0.30 ounces. You randomly select 45 cans and carefully measure the contents. The sample mean of the cans is 131.9 ounces.  Does the machine need to be reset?  Explain your reasoning.

20  A manufacturer claim that the life span of its tires is 50,000 miles.  You work for a consumer protection agency and you are testing these tires.  Assume the life spans of the tires are normally distributed.  You select 100 tires at random and test them.  The mean life span is 49,741 miles.  Assume σ = 900.  Complete parts (a) through (c)

a.  Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 49,741 miles of less?
(Round to four decimal places as needed)
b.  using your answer form part (a), what do you think of the manufacturer’s claim?
c.  ssuming the manufacturer’s claim is true, would it be unusual to have an individual tire with a life span of 49, 741 mile? Why or why not?

1. A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispenses has a mean of 122 ounces and a standard deviation of 0.30 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of cans is 121.9 ounces. Does the machine need to be reset? Explain your reasoning.

20  A manufacturer claims that the life span of its tires is 49,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed.  You select 100 tires at random and test them.  The mean life span is 48, 778 miles.  Assume σ = 900. Complete parts (a) through (c).

a.  Assuming the manufacturer’s claim is correct, what is the probability that the mean of the sample is 48,778 miles or less?
(Round to four decimal places as needed)
b.  Using your answer from part (a), what do you think of the manufacturer’s claim?.
c.  Assuming the manufacturer’s claim is true, would it be unusual to have an individual tire with a life span of 48,778 mile? Why or why not?

20. A manufacturer claims that the life spam of its tires is 49,000 miles. You work for a consumer protection agency and you are testing these tires. Assume the life spans of the tires are normally distributed. You select 100 tires at random and test them. The mean life span is 48,807 miles. Assume the mean = 800.

MATH 221 Homework Week 6

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1  Given the same sample statistics, which level of confidence would produce the widest confidence interval?

A.  90%
B.  98
C.  99%
D.  95%

1. Given the same sample statistics, which level of confidence would produce the widest confidence interval?

A.  99%
B.  95%
C.  98%
D.  90%

Use the values on the number line to find the sampling error.

The sampling error is

1. Use the following values to find the sampling error:
u = 25.36
x = 26.74

3  Find the margin of error for the given values of c, s, and n.
C=0.90, s=3.4, n=81
E= (Round to three decimal places as needed)

3  Find the margin of error for the given values of c, s, and n.
C=0.90, s=3.6, n=81

1. Find the margin of error for the given values of c,s, and n.
C = 0.95, S = 3.1, N = 64

E= (Round to three decimal places as needed)

4  Construct the confidence interval for the population mean µ.

A 98% confidence interval for µ is ( ) (Round to two decimal places as needed)

4  Construct the confidence interval for the population meanµ.

1. Construct the confidence interval for the population mean.
c = 0.90, x = 5.9, s = 0.8, and n = 44

A 98% confidence interval for µ is ( ),  (Round to two decimal places as needed)

5  Construct the confidence interval for the population mean µ.

A 90% confidence interval for µ is ( ). (Round to one decimal place as needed)

5  Construct the confidence interval for the population mean µ.

1. Construct the confidence interval for the population mean.
c = 0.90, x = 15.7, s = 10.0, and n = 80

A 98% confidence interval for µ is ( ). (Round to one decimal place as needed)

6  Use the confidence interval to find the estimated margin of error.  Then find the sample mean.
A biologist reports a confidence interval of (4.3,5.1) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is
The sample mean is

6  Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A biologist reports a confidence interval of (1.6,3.2) when estimating the mean height (in centimeters) of a sample of seedlings.

The estimated margin of error is
The sample mean is

1. Use the confidence interval to find the estimated margin of terror. Then find the mean.
A biologist reports a confidence interval of (4.7,5.1) when estimating the mean height of a sample of seedlings.

7  Find the minimum sample size n needed to estimate µ for the given values of c, s, and E
C=0.90, s=7.7, and E=1
Assume that a preliminary sample has at least 30 members
N= (Round up to the nearest whole number)
7  Find the minimum sample size n needed to estimate µ for the given values of c, s, and E.
C=0.95, s= 9.3, and E=1
Assume that a preliminary sample has at least 30 members
N= (Round up to the nearest whole number)

7.Find the minimum sample size needed to estimate u for the given values of c, s, and E.
C = 0.90, S = 9.5, E = 1

8.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. A random sample of 40 home theater systems has a mean price of \$118.00 and standard deviation is \$19.50

8  You are given the sample mean and the sample standard deviation.  Use this information to construct the 90% and 95% confidence intervals for the population mean.  Interpret the results and compare the widths of the confidence intervals.  If convenient, use technology to construct the confidence intervals.

A random sample of 55 home theater system has a mean price of \$135.00 and a standard deviation is \$15.70.
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is ( ) (Round to two decimal places as needed)
Construct a 95% confidence interval for the population mean.
The 95% confidence interval is ( ) (Round to two decimal places as needed)
Interpret the results. Choose the correct answer below.

A.  With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than 90%.
B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95%, confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than 90%.

8  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean.  Interpret the results and compare the widths of the confidence intervals.  If convenient, use technology to construct the confidence intervals.

A random sample of 60 home theater system has a mean price of \$115.00 and a standard deviation is \$15.10.
Construct a 90% confidence interval for the population mean.
The 90% confidence interval is () (Round to two decimal places as needed)
Construct a 95% confidence interval for the population mean.
The 95% confidence interval is () (Round to two decimal places as needed)

Interpret the results. Choose the correct answer below.

A. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than 90%.
B. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95%, confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than 90%.

9  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.
A random sample of 31 gas grills has a mean price of \$642.90 and a standard deviation of \$58.40.

The 90% confidence interval is ( ) (round to one decimal place as needed)
The 95% confidence interval is ( ) (round to one decimal place as needed)

Which interval is wider?  Choose the correct answer below.

A.  The 90% confidence interval
B.  The 95% confidence interval

9.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean.
A random sample of 46 gas grills has a mean price of \$639.50 and standard deviation of \$55.40

10  You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 33 eight-ounce servings of different juice drinks has a mean of 93.5 calories and a standard deviation of 41.5 calories.
The 90% confidence interval is ( ). (Round to 1 decimal place as needed.)

The 95% confidence interval is ( ). (Round to 1 decimal place as needed.)
Which interval is wider?

A.  The 95% confidence interval
B.  The 90% confidence interval

10.You are given the sample mean and sample standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean.
A random sample of 49 eight ounce servings of different drinks has a mean of 91.9 and standard deviation of 40.3

11  People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence? Initial survey results indicate that σ=11.7 books

A 90% confidence level requires subjects.

(Round up to the nearest whole number as needed)

11.People were polled on how many books they read the previous year. How many subjects are needed to estimate the # of books read the previous year within 1 book with 95% confidence. O = 15.5 books

12  A doctor wants to estimate the HDL cholesterol of all 20-to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 2 points with 99% confidence assuming σ=15.4? Suppose that the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?

A % confidence level requires subjects.
(Round up to the nearest whole number as needed)

A % confidence level requires subjects.

(Round up to the nearest whole number as needed)

How does the decrease in confidence affect the sample size required?

A.  The sample size is the same for all levels of confidence
B.  The lower the confidence level the larger the sample size
C.  The lower the confidence level the smaller the sample size

12.A doctor wants to estimate the HDL cholesterol of all 20-29 year olds females. How many subjects are needed to estimate the HDL within 2 points with 99% confidence assuming o = 14.3? Also find out 95% confidence.

13  Construct the indicated confidence interval for the population mean µ using (a) a t-distribution. (b) if you had incorrectly used a normal distribution, which interval would be wider?

(a) The 95% confidence interval using a t-distribution is ( )
(round to one decimal place as needed.)

(b) If you had incorrectly used a normal distribution, which interval would be wider?

A.  The t-distribution has the wider interval
B.  The normal distribution has the wider interval

14  In the following situation, assume the random variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for population mean. If convenient, use technology to construct the confidence interval.
(a) In a random sample of 10 adults from a nearby county, the mean waste generated per person per day was 4.65 pounds and the standard deviation was 1.48 pounds.
Repeat part (a), assuming the same statistics came from a sample size of 450. Compare the results.

(a) For the sample size of 10 adults, the 90% confidence interval is ( )
(Round to 2 decimal places as needed.)
(b) For the sample of 450 adults, the 90% confidence interval is ( )
(Round to 2 decimal places as needed.)

Choose the correct observation below

A. The interval from part (a), which uses the normal distribution, is narrower than the interval from part (b), which uses the t-distribution.
B. The interval from part (a), which uses the t-distribution, is wider than the interval from part (b), which uses the normal distribution.
C.  The interval from part (a), which uses the normal distribution, is wider than the interval from part (b), which uses the t-distribution.
D.  The interval from part (a), which uses the t-distribution, is narrower than the interval from part (b), which uses the normal distribution.

14.In a random sample of 10 adults from a nearby county, the mean waste generated per person per day was 4.58 pounds and standard deviation was 1.04 pounds. Repeat part A and assume the sample size is 450.

15  Use the given confidence interval to find the margin of error and the sample proportion.

(0.662,0.690)
E = (type an integer or a decimal.)

15.Use the given confidence interval to find the margin of error and the sample proportion.
(0.685, 0.713)

1. In a survey of 654 males aged 18-64, 399 say they have gone to a dentist in the last year. Construct a 90 and 95% confidence interval.

16  In a survey of 633 males from 18-64, 390 say they have gone to the dentist in the past year.
Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval for the population proportion p is ( )
(Round to 3 decimal places as needed.)
The 95% confidence interval for the population proportion p is ( )
(Round to 3 decimal places as needed.)

Interpret your results of both confidence intervals.

A.  With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.
B.  With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.
C.  With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.

Which interval is wider?

A.  The 90% confidence interval
B,  The 95% confidence interval

17  In a survey of 6000 women, 3431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.
A 99% confidence interval for the population proportion is ( )
(Round to 3 decimal places as needed)

17.In a survey of 9000 women, 6431 say they change their nail polish once a week. Construct a 99% confidence.

1. a researcher wants to estimate with 99% confidence the # of adults who have high speed internet access. Her estimate must be accurate within 5% of the true proportion.
A) find the minimum sample size needed, using a prior study that found 46% of the respondents said they have high-speed internet access.
B) no preliminary estimate is available. Find the minimum sample size needed.

18  A researcher wishes to estimate, with 99% confidence, the proportion of adults who have high-speedy internet access. Her estimate must be accurate within 4% of the true proportion.

a) Find the minimum sample size needed, using a prior study that found that 42% of the respondents said they have a high-speedy internet access.
b) No preliminary estimate is available. Find the minimum sample size needed.

A) What is the minimum sample size needed using a prior study that found that 42% of the respondents said they have high-speed internet access?
n = (Round up to the nearest whole # as needed.)
B) What is the minimum sample size needed assuming that no preliminary estimate is available?
n = (Round up to the nearest whole # as needed.)

MATH 221 Homework Week 7

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1. Use the given statement to represent a claim. Write it’s complement and state which is Ho and which is Ha.u > 635Find the complement of the claim.
u < 6351 Use the given statement to represent a claim. Write it’s complement and state which is Ho and which is Ha.u > 635Find the complement of the claim.
u < 635
2. A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right tailed, or two-tailed.
3. What type of test is being conducted in this problem?
1. A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right tailed, or two-tailed.

What type of test is being conducted in this problem?

1. Write the null and alternative hypotheses. Identify which is the claim.
A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 700 hours.

Identify which is the claim.

3 Write the null and alternative hypotheses. Identify which is the claim.
A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 700 hours.  Identify which is the claim.

4 Write the null and alternative hypotheses. Identify which is the claim. The standard deviation of the base price of a certain type of car is at least \$1010. Identify which is the claim.

1. Write the null and alternative hypotheses. Identify which is the claim. The standard deviation of the base price of a certain type of car is at least \$1010.Identify which is the claim.
1. More than 11% of all homeowners have a home security alarm. Determine whether the hypothesis for this claim is left-tailed, right-tailed, or two-tailed. Explain your reasoning.
2. A film developer claims that the mean number of pictures developed for a camera with 22 exposures is less than 17. If a hypothesis test is performed, how should interpret a decision that (a) rejects the null hypothesis and (B) fails to reject the null hypothesis?

A = There is enough evidence to support the claim that the mean number of pictures developed for a camera with 22 exposures is less than 17.
B = There is not enough evidence to support the claim that the mean number of pictures developed for a camera with 22 exposures is less than 17.

6 A film developer claims that the mean number of pictures developed for a camera with 24 exposures is less than 23. If a hypothesis test is performed, how should interpret a decision that (a) rejects the null hypothesis and (B) fails to reject the null hypothesis?

7 Find the P-value for the indicated hypothesis test with the given test statistic, z. Decide whether to reject Ho for the given level of significance a.
Two-tailed test with test statistic z = -2.08 and a = 0.04
P-Value =
Conclusion =

1. Find the P-value for the indicated hypothesis test with the given test statistic, z. Decide whether to reject Ho for the given level of significance a.
Two-tailed test with test statistic z = -2.08 and a = 0.04
P-Value =
Conclusion =
2. Find the critical z values. Assume that the normal distribution applies.
Right-tailed test, a =
Z =8 Find the critical z values. Assume that the normal distribution applies.
Right-tailed test, a =
Z =
3. Find the critical value(s) for a left-tailed z-test with a = 0.01. Include a graph with your answer.
Critical Value =

Graph:

9  Find the critical value(s) for a left-tailed z-test with a = 0.01. Include a graph with your answer.
Critical Value = -2.33

Graph:

1. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
Claim u =, a =, sample statistics: x =, s =, n =

Standardized test statistic =
Critical Values =

10 Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
Claim u = 50, a = 0.08, sample statistics: x = 49.2, s = 3.56, n = 80

1. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
Claim u = 5000, a = 0.05. Sample statistics x = 4800, s = 323, n = 46.Standardized test statistic =
Critical Values =
2. Test the claim about the population mean, u, at the given level of significance using the given sample statistics.
Claim u = 5000, a = 0.05. Sample statistics x = 4800, s = 323, n = 46.Standardized test statistic =
Critical Values =
12 A random sample of 85 eight grade students’ score on a national mathematics assessment test has a mean score of 275 with a standard deviation of 33. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on this exam is more than 270. At a = 0.03, is there enough evidence to support the administrators claim? Compare parts A – E.
3. A random sample of 85 eight grade students’ score on a national mathematics assessment test has a mean score of 275 with a standard deviation of 33. This test result prompts a state school administrator to declare that the mean score for the state’s eighth graders on this exam is more than 270. At a = 0.03, is there enough evidence to support the administrators claim? Compare parts A – E.

Z =
Area =
P Value =

1. A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 45 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of the cola has a mean caffeine content of 45.5 milligrams with a standard deviation of 6.1 milligrams. At a = 0.08, can you reject the company’s claim?

The critical values are =

z =

1. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 975 hours. A random sample of 72 light bulbs has a mean life of 954 hours with a standard deviation of 85 hours. Do you have enough evidence to reject the manufacturer’s claim? Use a = 0.04.

Zo =
Z =

1. An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to this test claim. You find that the mean waste recycled per person per day for a random sample of 12 adults in the country is 1.4 pounds and the standard deviation is 0.3 pound. At a = 0.10, can you support the claim? Assume the population is normally distributed.

To =

T =

15 An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 pound per person per day. You want to this test claim. You find that the mean waste recycled per person per day for a random sample of 12 adults in the country is 1.4 pounds and the standard deviation is 0.3 pound. At a = 0.10, can you support the claim? Assume the population is normally distributed.

16 A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 25 vehicles has a mean speed of 45 miles per hour and a standard deviation of 5.4 miles per hour. At a = 0.10, do you have enough evidence to support the county’s claim? Complete parts A – D.

1. A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 40 miles per hour. A random sample of 25 vehicles has a mean speed of 45 miles per hour and a standard deviation of 5.4 miles per hour. At a = 0.10, do you have enough evidence to support the county’s claim? Complete parts A through D.T =
P- Value =
2. A traveled association claims that the mean daily meal cost for two adults traveling together on vacation is \$100. A random sample of 20 such groups of adults has a mean daily meal cost of \$95 and a standard deviation of \$4.50. Is there enough evidence to reject the claim at a = 0.1? complete parts A – D.T =
P Value =
1. Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using given sample statistics.
Claim p = a = sample statistics: p = n =Can the normal sampling distribution be used?

The critical values are =
z =
What is the result of the test?

18 Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance a using given sample statistics.
Claim p = 0.23, a = 0.10, sample statistics: p = 0.18, n = 150.
Can the normal sampling distribution be used?

1. (a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis. An environmental agency recently claimed more than 25% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1000 customers, you find 40% have stopped buying the product. At a=0.03, do you have enough evidence to support the claim?

Zo = 1.88
Z =

19 (a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis. An environmental agency recently claimed more than 25% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1000 customers, you find 40% have stopped buying the product. At a=0.03, do you have enough evidence to support the claim?

20.  A humane society claims that less than 36% of U.S. households own a dog. In a random sample of 406 U.S. households, 154 say they own a dog. At a = 0.10, is there enough evidence to support the society’s claim?
(a) write the claim mathematically and identify Ho and Ha. (b) find the critical value(s) and identify the rejection region(s). (c) find the standardized test statistic. (d) decide whether to reject or fail to reject the null hypothesis, and € interpret the decision in the context of the original claim.

Critical Values =

A =

MATH 221Final Exam with ALL Formulas  ALL Answers are 100% Correct.

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#### This exam includes formulas in Word and in Excel, which can be used if numeric data is different from the one listed below.

The most recent final exam is available here:

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A+ Formulas in Excel included

1. The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d) (a)Find the probability that the student is male or a nursing major.

P (being male or being nursing major) =
(b) Find the probability that the student is female or not a nursing major.
P(being female or not being a nursing major) =
(c) Find the probability that the student is not female or a nursing major
P(not being female or not being a nursing major) =
(d) Are the events “being male” and “being a nursing major” mutually exclusive? Explain.

1. An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is \$22,325. The annual pay for a random sample of 10 full-time male workers over age 25 without a high school diploma is listed. At a = 0.10, test the claim that the mean salary is \$22,325. Assume the population is normally distributed.

20,660 – 21,134 – 22,359 – 21,398 – 22,974, – 16,919 – 19,152 – 23,193 – 24,181 – 26,281

(a) Write the claim mathematically and identify

Which of the following correctly states ?

(b) Find the critical value(s) and identify the rejection region(s).

What are the critical values?

Which of the following graphs best depicts the rejection region for this problem?

(c) Find the standardized test statistics.
t =

(d) Decide whether to reject or fail to reject the null hypothesis.
reject because the test statistics is in the rejection region.

a. fail to reject because the test statistic is not in the rejection region.
c. reject because the test statistic is not in the rejection region.
d. fail to reject  because the test statistic is in the rejection region.

(e) Interpret the decision in the context of the original claim.
a. there is sufficient evidence to reject the claim that the mean salary is \$22,325.
b. there is not sufficient evidence to reject the claim that the mean salary is not \$22,325.
c. there is sufficient evidence to reject the claim that the mean salary is not \$22,325.
d. there is not sufficient evidence to reject the claim that the mean salary is \$22,325.

1. The times per week a student uses a lab computer are normally distributed, with a mean of 6.1 hours and a standard deviation of 1.2 hours. A student is randomly selected. Find the following probabilities.
(a) The probability that the student uses a lab computer less than 5hrs a week.
(b) The probability that the student uses a lab computer between 6-8 hrs a week.

(c) The probability that the student uses a lab computer for more than 9 hrs a week.

(a) =
(b) =
(c) =

1. Write the null and alternative hypotheses. Identify which is the claim.
A study claims that the mean survival time for certain cancer patients treated immediately with chemo and radiation is 13 months.
2. Find the indicated probability using the standard normal distribution.
P(z>) =
3. The Gallup Organization contacts 1323 men who are 40-60 years of age and live in the US and asks whether or not they have seen their family doctor.What is the population in the study?
Answer:What is the sample in the study?
1. The ages of 10 brides at their first marriage are given below.
4 32.2     33.6     41.2     43.4     37.1     22.7     29.9     30.6     30.8(a) find the range of the data set.
Range =
(b) change 43.4 to 58.6 and find the range of the new date set.
Range =
1. The following appear on a physician’s intake form. Identify the level of measurement of the data.
(a) Martial Status
(b) Pain Level (0-10)
(c) Year of Birth
(d) Height(a) what is the level of measurement for marital status(b) what is the level of measurement for pain level(c) what is the level of measurement for year of birthWhat is the level of measurement for height
1. To determine her air quality, Miranda divides up her day into 3 parts; morning, afternoon, and evening. She then measures her air quality at 3 randomly selected times during each part of the day. What type of sampling is used?
1. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below.
• X= 150 calories
• X= 100 calories
• X = 120 calories
• X = 60 calories

Find the regression equation.
=
Choose the correct graph below.

(a) predict the value of y for x = 150.
(b) predict the value of y for x = 100.
(c) predict the value of y for x = 120.
(d) predict the value of y for x = 60.

11.  A restaurant association says the typical household spends a mean of \$4072 per year on food away from home. You are a consumer reporter for a national publication and want to test this claim. You randomly select 12 households and find out how much each spent on food away from home per year. Can you reject the restaurant association’s claim at a = 0.10? Complete parts a through d.

• Write the claim mathematically and identify. Choose the correct the answer below.

Use technology to find the P-value.
P =
Decide whether to reject or fail the null hypothesis.

Interpret the decision in the context of the original claim. Assume the population is normally distributed. Choose the correct answer below.

12.  The table below shows the results of a survey in which 147 families were asked if they own a computer and if they will be taking a summer vacation this year.

(a) find the probability that a randomly selected family is not taking a summer vacation year.
Probability =
(b) find the probability that a randomly selected family owns a computer
Probability =
(c) find the probability that a randomly selected family is taking a summer vacation this year and owns a computer
Probability =
(d) find the probability a randomly selected family is taking a summer vacation this year and owns a computer.
Probability =

• Are the events of owning a computer and taking a summer vacation this year independent or dependent events?
• 13. Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(5) when ᶙ = 4

P(5) =

14.  In a survey of 7000 women, 4431 say they change their nail polish once a week. Construct a 99% confidence interval for the population proportion of women who change their nail polish once a week.
A 99% confidence interval for the population proportion is…

15 A random sample of 53 200-meter swims has a mean time of 3.32 minutes and the population standard deviation is 0.06 minutes. Construct a 90% confidence interval for the population mean time. Interpret the results.
The 90% confidence interval is

Interpret these results. Choose the correct answer:
Answer: With 90% confidence, it can be said that the population mean time is between the end points of the given confidence interval.

16. Determine whether the variable is qualitative or quantitative: Weight

Quantitative
Qualitative

17. 32% of college students say that they use credit cards because of the reward program. You randomly select 10 college students and ask each to name the reason he or she uses credit cards. Find the probability that the number of college students who say they use credit cards because of the reward program is (a) exactly two, (b), more than two, and (c), between two and five inclusive.

(a) P(2) =
(b) P(X>2) =
(c) P(2<x<5) =

18.  A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 950 hours. A random sample of 74 light bulbs has a mean life of 943 hours with a standard deviation of 90 hours. Do you have enough evidence to reject the manufacturer’s claim? Use ᶏ = 0.04

• Identify the critical value(s).(c) identify the standardized test statistic.
z =
(d) decide whether to reject or fail to reject the null hypothesis.A. Reject . There is sufficient evidence to reject the claim that the bulb life is at least 950 hours.
B. Fail to reject . There is not sufficient evidence to reject the claim that the mean bulb life is at least 950 hours.
C. Fail to reject . There is sufficient evidence to reject the claim that mean bulb life is at least 950 hours.
D. Reject . There is not sufficient evidence to reject the claim that mean bulb life is at least 950 hours.19. Use technology to find the sample size, mean, medium, minimum data value, and maximum data value of the data. The data represents the amount (in dollars) made by several families during a community yard sale.
25 67.25 156      134.75 98.25   149.25 124.75 109.75 117      104.75 76The sample size is
The mean is
The medium is
The minimum data value is
The maximum data value is20. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed internet access. Her estimate must be accurate within 5% of the true proportion.
(a) find the minimum sample size needed, using a prior study that found 54% of the respondents said they have high-speed internet access.
(b) no preliminary estimate is available. Find the minimum sample size needed.(a) what is the minimum sample size needed using a prior study that found that 54% of the respondents said they have high-speed internet access?n =(b) what is the minimum sample size needed assuming that no preliminary estimate is available?n =21. You interview a random sample of 50 adults. The results of the survey show that 50% of the adults said they were more likely to buy a product where there are free samples. At ᶏ = 0.05, can you reject the claim that at least 54% of the adults are more likely to buy a product when there are free samples?State the null and alternative hypotheses. Choose the correct answer below.

Determine the critical value(s).

The critical value(s) is/are

find the z-test statistic.
z =

what is the result of the test?
A. reject . The data provide sufficient evidence to reject the claim.

1. fail to reject . The data provide sufficient evidence to reject the claim.
C. Reject . The data do not provide sufficient evidence to reject the claim.
D. fail to reject . The data do not provide sufficient evidence to reject the claim.

22.  The budget (in millions of dollars) and worldwide gross (in millions of dollars) for eight movies are shown below. Complete parts (a) through (c)

 Budget X 209 203 198 198 179 176 175 168 Gross Y 254 341 453 656 721 1049 1839 1267

(a) display the data in a scatter plot. Choose the correct graph below.

(b) calculate the correlation coefficient r.
r =

(c) make a conclusion about the type of correlation.
The correlation is a …linear correlation.

23.  A machine cuts plastic into sheets that are 30 feet (360 inches) long. Assume that the population of lengths is normally distributed. Complete parts a and b.

• The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch.
n =
Repeat part (a) using an error tolerance of 0.0625 inch.
n =

Which error tolerance requires a larger sample size? Explain.

A.  The tolerance E = 0.0625 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
B.  The tolerance E = 0.125 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
C.  The tolerance E = 0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.
D.  The tolerance E = 0.0.625 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.

MATH 221 Discussions Week 1-7 All  Posts 542 Pages 2 Sets

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The most recent discussions are available here:

MATH 221 Discussions Recent Week 1-7 All Posts 332 Pages DeVry

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MATH 221 Descriptive Statistics Discussions Week 1 All Post 75 Pages

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If you were given a large data set such as the sales over the last year of our top 1,000 customers, what might you be able to do with this data? What might be the benefits of describing the data?…

How is a sample related to a population?  Why is a sample used more often than a population?  What are some of the benefits of representing data sets using frequency distributions?  Do any of you use frequency distributions in your line of work?  Based on everything we’ve discussed, how might you create a sampling strategy that would more accurately reflect the purchases of all our customers?…

MATH 221 Regression Discussions Week 2 All Posts 79 Pages

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Suppose you are given data from a survey showing the IQ of each person interviewed and the IQ of his or her mother. That is all the information that you have. Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?…

Making a scatter plot is a good way to go.  You could certainly have no correlation, if no relationship truly exists between the two variables.

Positive correlation would equate to the higher the parent’s IQ, the higher the child’s.  What do you think?  What other independent variables could be added to the regression and why?  How would you know if the regression results were a good predictor of the dependent variable? What decisions could be made or insights provided through the regression results?…

MATH 221 Statistics in the News Discussions Week 3 All Posts 78 Pages

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Keep your eyes and ears open as you read or listen to the news this week. Find/discover an example of statistics in the news to discuss the following statement that represents one of the objectives of statistics analysis: “Statistics helps us make decisions based on data analysis.” Briefly discuss how the news item or article meets this objective. Cite your references….

Class, did any of you ever read the NUMBERS section in Time magazine? Here’s some good statistics on Aviation:

Minutes added to a Northwest Airlines transatlantic flight by flying 10 MPH slower, saving 162 gallons of fuel during the flight: 8

Projected savings in fuel costs that Southwest Airlines expects this year by reducing speeds, adding 1 to 3 minutes to its flights: \$42 million

This just blew my mind! One of the neat things about Statistics is its ability to make you think. I’m going to stop speeding on the freeway because of this information. What do you all think? Any other personal testimonials?

MATH 221 Discrete Probability Variables Discussions Week 4 All Post 79 Pages

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What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution? When might you use a geometric probability?  Give an example of a continuous random variable and a discrete random variable. Explain your answer….

Use the binomial probability table in the text to answer the following probability questions. According a study, the probability that a butterfly lives for over 2 days is 30%. In a random study of 9 butterflies, what is the probability that:

1. a) Exactly 4 are alive after 2 days?b) At least 4 are alive after 2 days?c) Less than 4 are alive after 2 days.

If X = {1, 9, 10, 15} and P(1) = .3, P(9) = .2, P(10) = .25, and P(15) = .25, can we call it a random variable for a probability distribution?

What if P(1) = .25, P(9) = .2, P(10) = .25, and P(15) = .25?…

MATH 221 Interpreting Normal Distributions Discussions Week 5 All Posts 82 Pages

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Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not? What’s a normal distribution?…

What about the sample size?  What does its magnitude give you relative to confidence in your response?

Explain what the *standard* normal distribution is.

b. What is a “z-score”?
c. Find the area under the standard normal curve to the left of z = -1.0
d. Find the area under the standard normal curve between z=-0.5 and z=1.5.

When you post your answer, *explain* what you did (for (c) and (d)). Please show your work so that everyone has a chance to understand…

MATH 221 Confidence Interval Concepts Discussions Week 6 All Posts 72 Pages

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Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula….

Class, can you think of how you might use statistical analysis/confidence intervals in your course of study?  We have several nursing students in this class.  Any applications there?…

MATH 221 Rejection Region Discussions Week 7 All Posts 77 Pages

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How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?…

A government worker claims that the standard deviation of the mean weight of all US Postal Service shipments is 0.40 pounds. If a hypothesis test is performed, how should you interpret a decision that

(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?

First we figure out what the hypotheses are here by this easy trick.

The claim is that the standard deviation (sigma) is equal to 0.40 pounds. Since it includes an “=” sign, it is the null hypothesis “H_0 : sigma = 0.40”. Thus, the…

Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?…

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