A bank officer wants to determine the amount of the average total monthly deposits per customer at the bank. He believes an estimate of this average using a confidence interval is sufficient.
a) How large a sample should he take to be within $200 of the actual average with 99% confidence? He assumes the standard deviation of total monthly deposits for all customers is about $1000.
b) What about 95%? How do the two results compare? Explain your answer.