Data made available through the Petersen-Kaiser Health System Tracker in May 2018 showed health expenditures were $10,348 per person in the United States. Use $10,348 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.
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 $12,000? If the survey research firm reports a sample mean greater than $12,000, would you question whether the firm followed correct sampling procedures? Why or why not?