Many schools require that applicants take a standardized test such as the Schola

Question

Many schools require that applicants take a standardized test such as the Scholastic Aptitute Test (SAT). The math part of this test is scored on a 200-800 scale and in theory, follows a normal distribution with a mean of 500 and a standard deviation of 100 (see below). Suppose that all applicants to a good business school in suburban Boston score between 600 and 700 (those with scores over 700 go to Bentley). Graphically, this would be the shaded area seen here: What would be median score of these applicants?

Explanation / Answer

median score of these applicants =mean score =(200+800)/2 =500

P(600<X<700)=P((600-500)/100<Z<(700-500)/100)=P(1<Z<2) =0.97725-0.84134=0.1359

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