mixed probability distributions 5157 The gradepoint averages

mixed probability distributions

5.157 The grade-point averages of a large population of college students are approximately distributed with a mean equal to 2.4 and a standard deviation equal to 0.5 a What fraction of the students possesses a grade-point average in excess of 3.0? b If students who possess a grade-point average equal to or less than 1.9 are dropped from college, what percentage of the students will be dropped? C Suppose that three students are selected at random from the student body. What is the probability that all three possess a grade-point average in excess of 3.0?

Solution

(A) P(X>3) = P((X-mean)/s >(3-2.4)/0.5)

=P(Z>1.2) =0.1151 (from standard normal table)

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(b) P(X<1.9) = P(Z<(1.9-2.4)/0.5) = P(Z<-1) = 0.1587 (from standard normal table)

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(c) The probability is 0.1151^3 =0.001524846