44. BusinessWeek surveyed MBAalumni 10 years after graduation (BusinessWeek, September 22, 2003). One finding was that alumni spend an average of $115.50 per week eating out socially. You have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni. Assume the population standard deviation is $35.

a. Show the sampling distribution of , the sample mean weekly expenditure for the 40 MBA alumni.

b. What is the probability the sample mean will be within $10 of the population mean?

c. Suppose you find a sample mean of $100. What is the probability of finding a sample mean of $100 or less? Would you consider this sample to be an unusually low spending group of alumni? Why or why not?