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. (a) Show the sampling distribution of the mean amount of health care expenditures in dollars for a sample of 100 people. O 9848 10098 10348 10598 10848 - 250 0 250 500 750 -500 -250 0 250 500 5348 7848 10348 12848 15348 O (b) What is the probability the sample mean will be within 1$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? Yes, because the probability that the sample mean will be greater than $12,600 is very small. Yes, because $12,600 is not within 1$100 of the population mean. No, because the probability that the sample mean will be greater than $12,600 is very large. O No, because $12,600 is within one standard deviation of $10,348