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. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 9,848, 10,098, 10,348, 10,598, 10,848. The curve enters the viewing window near 9,848 just above the horizontal axis and travels up to the right to a maximum near 10,348. After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 10,848. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 500, 250, 0, 250, 500. The curve enters the viewing window near 500 just above the horizontal axis and travels up to the right to a maximum near 0. After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 500. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 250, 0, 250, 500, 750. The curve enters the viewing window near 250 just above the horizontal axis and travels up to the right to a maximum near 250. After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near 750. A bell-shaped curve is above a horizontal axis labeled p. In order of left to right, the ticks on the horizontal axis are labeled: 5,348, 7,848, 10,348, 12,848, 15,348. The curve enters the viewing window near 5,348 just above the horizontal axis and travels up to the right to a maximum near 10,348. After reaching the maximum, the curve then travels down and to the right until it leaves the viewing window at the same height it entered near (b) What is the probability the sample mean will be within $100 of the population mean? (Round your answer to four decimal places.) 0.4514 Incorrect: Your answer is incorrect. (c) What is the probability the sample mean will be greater than $12,600? (Round your answer to four decimal places.) .