The times per week a student uses a lab computer are normall

The times per week a student uses a lab computer are normally distributed, with a mean of 6.6 hours and a standard deviation of 1.4 hours. A student is randomly selected.

Find the following probabilities.

(a) The probability that a student uses a lab computer less than 4 hours per week is . (Round to three decimal places as needed.)

(b) The probability that a student uses a lab computer between 7 and 9 hours per week is (Round to three decimal places as needed.)

(c) The probability that a student uses a lab computer more than 10 hours per week is. (Round to three decimal places as needed.)

Solution

(a) P(X<4) = P((X-mean)/s <(4-6.6)/1.4)

=P(Z<-1.86) =0.031 (from standard normal table)

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(b)P(7<X<9) = P((7-6.6)/1.4<Z<(9-6.6)/1.4)

=P(0.29<Z<1.71) =0.342(from standard normal table)

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(c)P(X>10) = P(Z>(10-6.6)/1.4)

=P(Z>2.43) =0.008(from standard normal table)