In examining the credit accounts of a department store, an auditor would like to estimate the true mean account error (book value – audited value). To do so, the auditor selected a random sample of 50 accounts and found the mean account error to be $60 with a standard deviation of $30.

a. Construct a 95% confidence interval for the population mean account error. What conclusion can be made from this confidence interval?

b. How large a sample is actually needed to ensure with 95% confidence in estimating the population mean account error to within ±$5?

c. Among the 50 selected accounts, the auditor found that there were 6 of them consisted of an account error of more than $100. Based on this information, construct a 99% confidence interval for the population proportion of accounts with an error of more than $100. What conclusion can be made from this confidence interval?