Each year the admissions commitee at a top business school recieves a large number of application for admission to the MBA program and they have to decide on the number of offer to make. Since sum of the admitted students may decide to persuit other opportunities, the commitee at typically admit more students than the ideal class size of 720 students. You were asked to help the admission commitee 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 not accept the admission offer is normally distributed with mean 50 and standard deviaion 21. Suppoe for now that the school doesn't maintain a waiting list, that is all studnets are accepted or rejected.
a. Suppose 750 students are admitted, what is the probability that the class size will be at least 720 students?
b. It is hard to associate a monetary value with admitting too many students or admitting too few. However, there is a mutual agreement that it is about 2 times more expensive to have a student in excess of the ideal 720 than to have fewer students in the class. What is the appropriate number of students to admit?
c. A waiting list mitigates the problme of having too few students since at the very last moment there is an opportunity to admit some students from the waiting list. Hence the admission committee revises its estimate: It claim that it is 5 times more expensive to have a students in excess of 720 than to have fewer students accept among the initial group of admitted students. What is your revise suggestion?