In 1999, the average fee paid by H&R Block tax preparation customers in Canada was $55.93. Assume that the standard deviation of fees was $20 but that we have no idea regarding the shape of the population distribution.
a. What additional assumption about the population would be needed in order to use the standard normal table in determining the probability that the mean fee for a simple random sample of 5 customers was less than $50?
b. What is the probability that the mean fee for a simple random sample of 36 customers was less than $50? What role does the central limit theorem play in making it possible to determine this probability?