The times per week a student uses a lab computer are normally distributed, with

Question

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) Find the probability that the student uses a lab computer less than 5 hours per week. (b) Find the probability that the student uses a lab computer between 7 and 9 hours per week. (c) Find the probability that the student uses a lab computer more than 10 hours per week. (a) The probability that a student uses a lab computer less than 5 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.)

Explanation / Answer

Mean = 6.6 hours

Standard deviation = 1.4 hours

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(less than 5 hours a week) = P(X < 5)

= P(Z < (5 - 6.6)/1.4)

= P(Z < -1.14)

= 0.127

b) P(7 < X < 9) = P(X < 9) - P(X < 7)

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

= P(Z < 1.71) - P(Z < 0.29)

= 0.956 - 0.614

= 0.342

c) P(X > 10)

= 1 - P(X < 10)

= 1 - P(Z < (10-6.6)/1.4)

= 1 - P(Z < 2.43)

= 1 - 0.992

= 0.008

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