In: Statistics and Probability
2. The latest available data showed health expenditures were $8086 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) Identify the sampling distribution of the mean amount of health care expenditures for a sample of 100 people. (1.5 marks) b) What is the probability the sample mean will be within ±$200 of the population mean? (1 mark) c) What is the probability the sample mean will be greater than $9000? If the survey research firm reports a sample mean greater than $9000, would you question whether the firm followed correct sampling procedures? Why or why not? (0.5 + 0.5 mark).