In 2009, the average fee paid by H&R Block tax preparation customers was $187. Assume that the standard deviation of fees was $60 but that we have no idea regarding the shape of the population distribution.
Source: hrblock.com, July 14, 2009.
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 $170?
b. What is the probability that the mean fee for a simple random sample of 36 customers was less than $170? What role does the central limit theorem play in making it possible to determine this probability?