A college changes their recruiting by giving rewards for good examination scores

Question

A college changes their recruiting by giving rewards for good examination scores on entry. New students can earn a max of 100, anyone who scores more than 80 on the examination are compensated $1500 towards books or classes. Students who score from 60 to 80 are compensated $600. Students who score less than 60 unfortunately do not get compensated. Given, examination scores are normally distributed with ^2 = 45 and = 73.

The college will not process prospective students who have scores in the bottom 45% of all new students. Find the examination score that a prospective student must get in order to be considered for continued processing. Please explain, draw diagram if possible.

Explanation / Answer

here std deviation =(45)1/2 =6.708

for 45 percentile from normal distribution curve ; zscore =-0.1257

as to be considered a student must have higher standardized z score

therefore corresponding score =mean +z*std deviation =73-0.1257*6.708 =72.16

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