The mean score of a college entrance test is 515 the standar

The mean score of a college entrance test is 515; the standard deviation is 81. The scores are normally distributed. What percent of the students scored below 328?

Solution

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The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320?

About 50.82%

About 34.13%

About 7.86%

About 0.82%

Answer

The percent of the students scored below 320 is

P(X<320) = P((X-mean)/s <(320-500)/75)

=P(Z<-2.4) =0.0082 (from standard normal table)

So answer is About 0.82%