Solve the problem.
-A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected,
Find the probability that their mean rebuild time exceeds 7.7 hours.
A) 0.9712
B) 0.9931
C) 0.9634
D) 0.8531

Question

Quizplus · Accepted Answer

We use the central limit theorem since sample size n=40>30. 
z=(x̄-μ)/(σ/√n)=(7.7-8.4)/(1.8/√40)=-2.63
P(z>-2.63)=0.9943
The probability that their mean rebuild time exceeds 7.7 hours is the same as the probability that the mean rebuild time is less than or equal to 7.7 hours. Thus, the answer is 1-0.9943=0.0057. However, the question asks for the probability that the mean rebuild time exceeds 7.7 hours, so we need to subtract from 1 again.
1-0.0057=0.9943 which is closest to choice B.

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