Your team is advising the college admissions office on how many student to admit from the pool of 25k applicants. The office tells you that historically, about 30% of admitted students matriculate to this residential college (almost all student live on campus). The Admission office believes is should admit 10k.
The college bursar needs to college the $20,000 tuition (assume all student pay the same) from 3k students to meet the $60 million target for incoming students for the will not be enough to meet the budget.
The housing director informs you that up to 4k dorm rooms are available for incoming students. If the college offers admission to 10k students,
A. what is the probability that the bursar will not reach the $60 million target--(fewer than 3k accept the offer)?
B. what is the probability that the housing director will run out of housing (more than 4k accept the offer)?
C. What is YOUR advice to the admissions office on how many students to admit, and why?
