Q3} ............................................................................................... 12 marks Suppose that a committee is studying whether or not there is a waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 36 people who recently served as jurors. The sample average wait time was ve hours with a sample standard deviation of two hours. (a) (1 pt) In words, what do the random variables X and 3 represent? (b) (2 pts) Which distributions should you use for X and J? respectively, if applicable? Explain your choice. Note that a population standard deviation is not provided. (c) (3 pts) What sample size is needed to be 90% confident of being correct within a half hour of the average wait time given that the population standard deviation o = 2 hours?(d) (6 pts) Construct a 95% condence interval for the population mean time wasted in the following two cases: 1. The standard deviation of the population is supposed to be the same as the sample standard deviation. 2. The underlying distribution of X is assumed to be normal distribution with unknown standard deviation. The committee randomly surveyed only 11 = 15 people