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...

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 amount using a confidence interval is sufficient. He assumes the standard deviation of total monthly deposits for all customers is about $1,475. How large a sample should he take to be within $200 of the actual average with 95% confidence?