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 9.1 hours.
A) 0.1285
B) 0.1046
C) 0.0046
D) 0.0069

Question

Quizplus · Accepted Answer

We can use the central limit theorem since the sample size, n is greater than 30. 
z = (x̄ - μ) / (σ/√n)
z = (9.1 - 8.4) / (1.8/√40)
z = 2.20
Using a standard normal distribution table, we find that the probability of z being greater than 2.20 is 0.0134. However, since we are looking for the probability that the mean rebuild time exceeds 9.1 hours (which is a one-tailed test), we need to find the area to the right of the z-value. 
Therefore, the probability that their mean rebuild time exceeds 9.1 hours is 0.0069, which is closest to choice D (0.0069).

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