The auditor needs to provide a confidence interval for the mean outstanding balance for a company's clients. From past experience, the distribution of outstanding balances is known to have a variance of 25. Assuming the population distribution of outstanding balances is normal,
(a) Find the 90% confidence interval for the mean outstanding balance if the auditor's sample of 65 accounts produced a sample mean of $140? Do you need to assume normality for the population distribution to answer the question? Explain.
(b) Suppose that before the survey is undertaken, the auditor wants to ensure that the 95% confidence interval for the mean outstanding balance that ends up with a total width of no more than 0.5. How many people should the auditor has sought to survey?