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 $8086 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 $2500.
a. Show the sampling distribution of the mean amount of health care expenditures for a sample of 100 people. Round your answer to nearest whole value.
b. What is the probability the sample mean will be within ± $200 of the population mean? Round your answer to four decimal places.
c. What is the probability the sample mean will be greater than $9000? Round your answer to four decimal places.