1 pt 13 of 20 (14 The Smes per week a uses a lab computer are normally distribut

Question

1 pt 13 of 20 (14 The Smes per week a uses a lab computer are normally distributed, with a mean of 6.4 hours and a standard deviation of 1.1 hours. A (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 (c) Find the probability that the student uses a lab computer more than 9 hours per week (Round to three decimall places as needed ) Round to three decimal places as needed ) (c) The probabiliy that a student uses a lab computer more than 9 hours per week i Round to three decimal places as needed) Type here to search prn sc 3

Explanation / Answer

Solution:- mean = 6.4 hours , sd = 1.1 hours

a) The probability that a student uses a lab computer less than 5 hours per week is 0.102
P(X < 5) = P(Z < (X - )/ )
= P(Z < (5 - 6.4)/1.1)
= P(Z < -1.2727)
= 1 P(Z < 1.2727)
= 1 0.898
= 0.102

b) The probability that a student uses a lab computer between 7 and 8 hours per week is 0.218
P(7 < X < 8) = P((7 - 6.4)/1.1 < Z < (8 - 6.4)/1.1)
= P(0.5454 < Z < 1.4545)
= 0.2177
= 0.218(rounded)

c) The probability that a student uses a lab computer more than 9 hours per week is 0.009
P(X > 9) = P(Z > (9 - 6.4)/1.1)
= P(Z > 2.3636)
= 1 P(Z < 2.3636)
= 1 0.9909
= 0.0091
= 0.009(rounded)

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