6117 Given that the data follows the normal probability dist

6.117 Given that the data follows the normal probability distribution with mean of 100 and standard deviation of 15, find the value of a such that:

Solution

(a) P(X<=110) = P((X-mean)/s <(110-100)/15)

=P(Z<0.67) =0.7486 (from standard normal table)

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(b)P(X>=110) = P(Z>0.67) =0.2514(from standard normal table)

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(c)P(70<=X<=110) = P((70-100)/15<Z<(110-100)/15)

=P(-2<Z<0.67) =0.7258(from standard normal table)

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(d)P(X<=80) = P(Z<(80-100)/15)

=P(Z<-1.33) = 0.0918 (from standard normal table)

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(e)P(65<=X<=90) = P((65-100)/15<Z<(90-100)/15)

=P(-2.33<Z<-0.67) =0.2415(from standard normal table)