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 5.8 hours and a standard deviation of 1.3 hours. A student is randomly selected. Find the following probabilities (a Find the probability that the student uses a lab computer less than 3 hours per week. (b Find the probability that the student uses a lab computer between 6 and 7 hours per week. c Find the probability that the student uses a lab computer more than 9 hours per week (a The probability that a student uses a lab computer less than 3 hours per week is (Round to three decimal places as needed. (b) The probability that a student uses a lab computer between 6 and 7 hours per week is (Round to three decimal places as needed. (c The probability that a student uses a lab computer more than 9 hours per week is (Round to three decimal places as needed.

Solution

(a)P(X<3)=P((X-mean)/s <(3-5.8)/1.3)

=P(Z<-2.15)

=0.016 (from standard normal table)

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(b)P(6<X<7) = P((6-5.8)/1.3<Z<(7-5.8)/1.3)

=P(0.15<Z<0.92)

=0.262 (from standard normal table)

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(c) P(X>9) = P(Z>(9-5.8)/1.3)

=P(Z>2.46)

=0.007 (from standard normal table)