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 5.9 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 4 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 4 hours per week is (Round to three decimal places as needed.)

Explanation / Answer

Solution:

(a) Find the probability that the student uses a lab computer less than 4 hours per week.
given ? = 5.9, ? = 1.4
P(x < 4) =
z = x - ?/? = (4 - 5.9)/1.4 = -1.36
P(Z < -1.36) = 0.0869 = 8.69%

(b) Find the probability that the student uses a lab computer between 6 and 7 hours per week.
given ? = 5.9 and ? = 1.4
P ( 6 < X < 7 ) = P ( 6?5.9/1.4 < X??/? < 7?5.9/1.4)
= P ( 0.07 < Z < 0.79 )
= 0.2573
(c) Find the probability that the student uses a lab computer more than 9 hours per week.
given ?=5.9 and ? = 1.4
P ( X > 9 ) = P ( X??/? > 9?5.9/1.4)
= P ( Z > 2.21 )
= 0.0136

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