Counselors at an exclusive private college look carefully at the applications fr

Question

Counselors at an exclusive private college look carefully at the applications from high school students seeking admission to the college. One of their criteria is that these students must score in the top 3.5% of all students who took the required entrance exam. The exam is constructed such that the scores are normally distributed with an average of 1200 and a standard deviation of 95 The minimum exam score necessary for applicants to be further considered for admission is Hint: I know you guys hate to do this because you think it's a waste of your time but y'all should really draw an appropriate diagram Note: Round all answers to the nearest integer

Explanation / Answer

P(X>=c) = .035, which means that person should be in top 3.5%

Z = 1.81 for cumulative probability of 1-.035 = .965

So, P(Z>=c) = .035,

P(Z<c) = 1-.035 = .965, Z = 1.81

(c-1200)/95 = 1.81

c = 1.81*95 + 1200

= 1371.95

So, minimum score necessary for applicants to be further considered for admission is 1371.95

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