You may need to use the appropriate technology to answer this question. 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. X -500 -250 0 250 500 O -250 0 250 500 750 5348 7848 10348 12848 15348 9848 10098 10348 10598 10848 O (b) What is the probability the sample mean will be within 1$150 of the population mean? (Round your answer to four decimal places.) 0.4515 (c) What is the probability the sample mean will be greater than $12,600? (Round your answer to four decimal places.) 9.01 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? O Yes, because the probability that the sample mean will be greater than $12,600 is very small. No, because $12,600 is within one standard deviation of $10,348. O Yes, because $12,600 is not within 1$150 of the population mean. O No, because the probability that the sample mean will be greater than $12,600 is very large.You may need to use the appropriate appendix table or technology to answer this question. After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of 50 USC students will be taken from this population. (a) What is the value of the standard error of the mean? (Round your answer to the nearest whole number.) $ 1047 (b) What is the probability that the sample mean will be more than $27,175? 0.5 (c) What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.) 0.7669 1X (d) What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.) 0.9094 1X