Counselors at an exclusive private college look carefully at

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 1000 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.

Solution

Top 2.5% means, they must be where the probability is 1 - 2.5% = 1 - 0.025 = 0.975

Average = u = 1000

SD = 95

USing http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf :

When z = 0.975, we get z = 1.96

1.96 = (x - u) / SD

1.96 = (x - 1000) / 95

x - 1000 = 95 * 1.96

x = 1000 + 95*1.96

x = 1186.2

So, the minimum necessary is 1186(rounded to integer)