2. (15 points) Each year the admission committee at a top business school receives a large number of applications for admission to its famous Master program and they have to decide on the number of offers to make. Since some of the admitted students may decide to pursue other opportunities and thus turn down the offer, the committee typically sends offers to more students than the ideal class size of 720 students. You were asked to help the admission committee estimate the appropriate number of people who should be offered admission. It is estimated that in the coming year the number of people who will turn down the admission offer is normally distributed with mean 50 and standard deviation 21. Suppose that the school does not maintain a waiting list that is, all students are either accepted or rejected. It is hard to associate a monetary value with admitting too many students or admitting too few. However, there is a mutual agreement that having a student in excess of the ideal size of 720 is four times as expensive as having a student short of the ideal number. What is the appropriate number of students to admit