The mean preparation fee H&R Block charged retail customers in 2012 was $273 (The Wall Street Journal). Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

A. What is the probability that the mean price of a sample of 30 H&R Block real customers is within $16 of the population mean?

B. What is the probability that the mean price for a sample of 50 H&R Block retail customers is within $16 of the population mean?

C. What is the probability that the mean price for a sample of 100 H&R Block customers is within $16 of the population mean?

D. Which, if any, of the sample sizes in parts a, b, and c would you recommend to have at least of a 0.95 probability that the sample mean is within $16 of the population mean?