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 2.5% of all students who took the required entrance exam. The exam is constructed such that the scores are normally distributed with an average of 1500 and a standard deviation of 150 The minimum exam score necessary for applicants to be further considered for admission is: round your answer to the nearest integer)

Explanation / Answer

mean = 1500 and sd = 150

Here, we are interested in upper tail of the normal curve.
find the z-value using right tailed z-table for which the area under curve is 0.025
z-value = 1.96

using central limit theorem,
x = 1500 + 1.96*150
x = 1794

Hence the minimum score required is 1794

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