More than 10,000 customers shop at your store each day. A sample of customers (n = 20) taken from the total population with a normal distribution results in an empirical variance of S² = 10² min² for the amount of time a customer spends in your store.

(a) Calculate the 99% confidence interval for the empirical variance.

(b) Calculate the two-sided 95% confidence interval for the average time a customer stays in your business. A sample size of n = 20 results in an average stay of 55 min.

(c) How large must the sample be so that a two-sided confidence interval of 95% of the average stay is no more than 4 min?