Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. a. What kind of a distribution does X have (name and values of all parameters)? b. Compute c. Calculate the mean value and standard deviation of X.

Answer: Step 1 of 3 Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. a. Here, X follows hypergeometric distribution. There are N individuals, N = 18 Out of which 18 are first time test takers (we’re going to think of being a first timer as a success) Out of those 18 we need to select 6 people and every subset is equally likely and we want to know how likely is that we selected a certain number of first timers. Taking everything mentioned above into consideration we can see that this is a hypergeometric distribution, where h(x;n, M,N) = h(x;6, 8, 18).