The admissions office of a small college is asked to accept deposits from a number of qualified prospective freshmen so that, with probability about .95, the size of the freshman class will be less than or equal to 120. Suppose the applicants constitute a random sample from a population of applicants, 80% of whom would actually enter the freshman class if accepted.
a. How many deposits should the admissions counselor accept?
b. If applicants in the number determined in part a are accepted, what is the probability that the freshman class size will be less than 105?