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

The mean preparation fee H&R Block charged retail customers in 2012 was $183. Use this price as the population means 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 if 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 to have at least a .95 probability that the sample mean is within $8 of the population mean?