Suppose data made available through a health system tracker 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 $2,500.
(b) What is the probability the sample mean will be within ±$100 of the population mean? (Round your answer to four decimal places.)
(c) What is the probability the sample mean will be greater than $12,600? (Round your answer to four decimal places.)
If the survey research firm reports a sample mean greater than $12,600, would you question whether the firm followed correct sampling procedures? Why or why not?
A) No, because $12,600 is within one standard deviation of $10,348.
B) No, because the probability that the sample mean will be greater than $12,600 is very large.
C) Yes, because $12,600 is not within ±$100 of the population mean.
D) Yes, because the probability that the sample mean will be greater than $12,600 is very small.
