6.80 The First-Year Class The admissions office of a small university is asked to accept deposits from a number of qualified prospective first-year students so that, with probability about 0.95, the size of the first year 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 first-year class if accepted.

a. How many deposits should the admissions counsel- lor accept?

b. If applicants in the number determined in part a are accepted, what is the probability that the first-year class size will be less than 105?