Question 1. According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send} IRS Form 1040 is 10.53 hours {without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. (a) Suppose 2X =The total length of time for 36 taxpayers to complete IRS Form 1040. What is the distribution of E X?{Show your calculations and formulas) (b) What is the probability that the total length of time for 36 taxpayers to complete IRS Form is between 380 and 385 hours? {Show your calculations, formulas and the curve) (c) What is the probability that the total length of time for 36 taxpayers to complete IRS Form is more than 390 hours? (Show your calculations, formulas and the curve) (d) Find the 75\"1 percentile for the total length oftime for 36 taxpayers. (Show your calculations and formulas) Question 2. Suppose that a category of world-class runners is known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let f the average of the 49 races. {a} Xn- [ , ). {Show your calculations and formulas) {b} Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons. (Show your calculations, formulas and the curve) {c} Find the 80\"1 percentile and 25'h percentile for the average of these 49 marathons. (Show your calculations, formulas and the curve) {d} Find the median of the average running times. (Show your calculations, formulas and the curve) Question 3. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the average amount oftime individuals waste at the courthouse waiting to be called for service. The committee randomly surveyed 31 people. The sample average was 8 hours with a sample standard deviation of4 hours. {3) Construct an 95% confidence interval for the population average time wasted and write the interpretation {Sketch the graph). {b) Which distribution you used for this problem? Explain your choice. Question 4. Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 97% confidence interval for the mean height of male Swedes. Forty-nine male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches. {3) Construct a 97% confidence interval for the population mean height of male Swedes and write the interpretation (Sketch the graph). {b) Which distribution you used for this problem? Explain your choice