MATH 221 Quiz Week 7 Recent

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MATH 221 Quiz Week 7 Recent
A researcher wishes to​ estimate, with 90​% confidence, the population proportion of adults…

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MATH 221 Quiz Week 7 Recent

MATH 221 Quiz Week 7 Recent

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  1. A researcher wishes to​ estimate, with 90​% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 4​% of the population proportion.

​(a) No preliminary estimate is available. Find the minimum sample size needed.

​(b) Find the minimum sample size​ needed, using a prior study that found that 44​% of the respondents said their favorite flavor of ice cream is chocolate.

​(c) Compare the results from parts​ (a) and​ (b).

A =
B =
C = Having an estimate of the population proportion…

  1. 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 4 points with 99% confidence assuming o = 16.1? suppose the doctor would be content with 95% confidence, how does the decrease in confidence affect the sample size required?

99% =
95 =
How does the decrease in confidence affect the sample size required? =…

  1. Construct the indicated confidence interval for the population mean μ using the​ t-distribution.

4. 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.

The probability that the member selected is…

  1. 5. You are given the sample mean and the population 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 41 gas grills has a mean price of $644.50 Assume the population standard deviation is $55.40.

The 90% confidence interval is
The 95% confidence interval is

  1. 6. A manufacturer claims that the life span of its tires is 51,000 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 50,740 miles. Assume σ=900900.

Complete parts​ (a) through​ (c).

  1. 7. Use the normal distribution of SAT critical reading scores for which the mean is 502 and the standard deviation is 118.

8. The table to the right shows the results of a survey in which 400 adults from the​ East, 400 adults from the​ South, 400 adults from the​ Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts​ (a) and​ (b).

Construct a 99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem

Construct a 99% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem. Is it possible that these two proportions are equal?  Explain your reasoning

9. 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 $65,500. A random sample of 31 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,500​? Assume σ=​$6,400.

Probability =…

  1. 10. Assume the random variable x is normally distributed with mean μ=88 and standard deviation σ=4.

Find the indicated probability.

​P(x < than<86​)

P(x <86​)=

  1. 11. A vending machine dispenses coffee into a twelve​-ounce The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.04 ounce. You can allow the cup to overfill 2% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?
  2. 12. The time spent​ (in days) waiting for a kidney transplant for people ages​ 35-49 can be approximiated by the normal​ distribution, as shown in the figure to the right.

​(a) What waiting time represents the 99th percentile?

​(b) What waiting time represents the first​ quartile?

  1. 13. A population has a mean μ=7979 and a standard deviation σ=1818.

Find the mean and standard deviation of a sampling distribution of sample means with sample size

n=3636.

  1. 14. In a random sample of 35 refrigerators, the mean repair cost was $119.00 and the population standard deviation is $15.10. Construct a 95​% confidence interval for the population mean repair cost. Interpret the results.

95% confidence =
With 95% confidence…

  1. 15. 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.

99% confidence =…

  1. 16. In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 3 and a standard deviation of 6.9.

Complete parts​ (a) through​ (d) below.

A =
B =
C =
D = The…

  1. 17. In a random sample of 21 people, the mean commute time to work was 7 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.

U =
Margin of error =
With 95% confidence…

  1. 18. In a survey of 661 males ages​ 18-64, 397 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.

90% =
95% =
B =

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

Quiz Week 7 Recent

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