The mean preparation fee H&R Block charged retail customers last year was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume the population standard deviation of preparation fees is $50.

a. What is the probability that the mean price for a sample of 30 H&R Block retail customers is within $8 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 $8 of the population mean?

c. What is the probability that the mean price for a sample of 100 H&R Block retail customers is within $8 of the population mean?

d. Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend having at least a .95 probability that the sample mean is within $8 of the population mean?