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 6.1 hours and a standard deviation of 1.2 hours. A student is randomly selt 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 6 and 8 hours per week. (c) Find the probability that the student uses a lab computer more than 9 hours per week (a) The probablity 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 6 and 8 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) Enter your answer in each of the answer boxes.

Explanation / Answer

Solution:- given mean= 6.1h , sd =1.2h

a) The probability that a stident use a lab computer less than 5 hours per week is 0.179

=> P(X < 5 ) = P(Z < (X - )/)

= P(Z < (5 - 6.1)/1.2)

= P(Z < -0.9166)

= 1 P(Z < 0.9166)
= 1 0.8212
= 0.1788

b. The probability that a student uses a lab computer between 6 and 8 hours per week is 0.475
=> P(6 < X < 8) = P((6-6.1)/1.2 < Z < (8-6.1)/1.2)
= P(0.0833 < Z < 1.5833)
= P(Z < 1.5833) P(Z < 0.0833)
= 0.9429 - 0.4681
= 0.4748

= 0.475(rounded)

The probability that a student uses a lab computer more than 9 hours per week is 0.008
=> P(X > 9) = P(Z > (9-6.1)/1.2)
= P(Z > 2.4167)
= 1 P(Z < 2.4167)
= 1 0.9922
= 0.0078
= 0.008(rounded)

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