Foot Locker uses sales per square foot as a measure of store productivity. Sales are currently running at an annual rate of $406 per square foot (The Wall Street Journal, March 7, 2012). You have been asked by management to conduct a study of a sample of 64 Foot Locker stores. Assume the standard deviation in annual sales per square foot for the population of all 3400 Foot Locker stores is $80.

a. Show the sampling distribution of x, the sample mean annual sales per square foot for a sample of 64 Foot Locker stores.

b. What is the probability that the sample mean will be within $15 of the population mean?

c. Suppose you find a sample mean of $380. What is the probability of finding a sample mean of $380 or less? Would you consider such a sample to be an unusually low performing group of stores?