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?

Given the question:

The mean tax-return 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.

Round your answers to four decimal places.

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?

Part A:

The probability that a sample of size, n, of a normally distributed data with a mean of μ, and standard deviation of σ, is within, a, units of the mean is given by

 

Thus, the probability that the mean price for a sample of 30 H&R Block retail customers is within $8 of the population mean is given by:



Part B:

The probability that the mean price for a sample of 50 H&R Block retail customers is within $8 of the population mean is given by:



Part C:

The probability that the mean price for a sample of 50 H&R Block retail customers is within $8 of the population mean is given by: