In the population of students who took the Graduate Record E

In the population of students who took the. Graduate Record Exam in a particular year,the \"analytical ability \"scores normally distributed with a mean of 520 and a standard deviation of 10. Suppose a particular college program will admit only those who scored in the top 25%. What is the minimum GRE score a person would need to earn in order to get into that program?

Solution

Suppose X is the GRE score. So X~N(520,10). The college will admit only those who scored in top 25% meaning that a student will be selected only if his marks( say X) is such that P(X>x)=.25 where \"x\" is the number of the students scored more than him. By definition this is the 3rd quartile of a Normal distribution which is given by. Now for a N(0,1) distribution Q3 the 3rd quartile is .68. For the N(520,10) distribution the 3rd quartile =520+10*.68=526.8. Required answer is 526.8