1. Data collected by oxford University’s Admissions Office has shown that about

Question

1. Data collected by oxford University’s Admissions Office has shown that about 65% of applicants offered admission accept the offer and matriculate as students. Because of this oxford “over admits”, in other words, admissions letters are sent to more applicants than the desired size of the first-year class. However, over-admitting does run the risk of having too many students in the class which increases class sizes and may require hiring adjunct faculty to take additional sections of first-year courses. For the 2017-18 admissions season, Oxford University is aiming to admit 275 students into the class of 2022. If the university would like to keep the probability of more than 275 students accepting admissions offers to 0.05, how many admissions letters should be sent out?

Explanation / Answer

Let say there are N admission letter that would be sent out so it would tell that the the probability of more than 275 students accepting the admission offer shall be equal to 0.05.

WHen proportion of applicants offered admission accept the offer = 0.65

Mean or expected number of people to accept letter = 0.65 N

standard deviation of the number of people accepting the letter = sqrt (0.65 * 0.35 * N) = 0.477N

So, Pr(X > 275; 0.65N ; 0.477N ) < 0.05

so from Z - table the value of Z for p - value 0.05 is

Z = 1.645

so (275 - 0.65N)/ 0.477N = 1.645

(275 - 0.65N)2 = 0.6157N

75625 + 0.4225 N2 - 357.5 N - 0.6157N = 0

0.4225 N2 - 358.12N + 75625 = 0

N = 448.74 ; 398.88

so we will reject the 448 value as it has 0.65N vvalue greater than 275 so

N = 398.88 and by ading 0.5 for continutity factor we will get

N = 399

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