The latest available data showed health expenditures were $8,086 per person in the United States or 17.6% of gross domestic product (Centers for Medicare & Medicaid Services website, April 1, 2012). Use $8,086 as the population mean and suppose a survey research firm will take a sample of 100 people to investigate the nature of their health expenditures. Assume the population standard deviation is $2,500.

a. Show the sampling distribution of the mean amount of health care expenditures for a sample of 100 people.

b. What is the probability the sample mean will be within ±$200 of the population mean?

c. What is the probability the sample mean will be greater than $9,000? If the survey research firm reports a sample mean greater than $9,000, would you question whether the firm followed correct sampling procedures? Why or why not?