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# Statistics: Problems and Solutions

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22. List the reasons for sampling. Give an example of each reason for sampling.

34. Information from the American Institute of Insurance indicates the mean amount of life
insurance per household in the United States is \$110,000. This distribution follows the
normal distribution with a standard deviation of \$40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?
b. What is the expected shape of the distribution of the sample mean?
c. What is the likelihood of selecting a sample with a mean of at least \$112,000?
d. What is the likelihood of selecting a sample with a mean of more than \$100,000?
e. Find the likelihood of selecting a sample with a mean of more than \$100,000 but less
than \$112,000.

32. A state meat inspector in Iowa has been given the assignment of estimating the mean
net weight of packages of ground chuck labeled â??3 pounds.â? Of course, he realizes that
the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean
weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.
a. What is the estimated population mean?
b. Determine a 95 percent confidence interval for the population mean.

34. A recent survey of 50 executives who were laid off from their previous position revealed
it took a mean of 26 weeks for them to find another position. The standard deviation of
the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population
mean. Is it reasonable that the population mean is 28 weeks? Justify your answer.

46. As a condition of employment, Fashion Industries applicants must pass a drug test. Of the
last 220 applicants 14 failed the test. Develop a 99 percent confidence interval for the proportion
of applicants that fail the test. Would it be reasonable to conclude that more than
10 percent of the applicants are now failing the test? In addition to the testing of applicants,
Fashion Industries randomly tests its employees throughout the year. Last year in the 400
random tests conducted, 14 employees failed the test. Would it be reasonable to conclude
that less than 5 percent of the employees are not able to pass the random drug test?