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) 0.8531
C) 0.9634
D) 0.9931

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will be approximately normal with mean 8.4 and standard deviation 1.8/sqrt(40). Using the z-score formula, we find the probability that the sample mean exceeds 7.7 hours, which corresponds to a z-score of approximately 2.48, leading to a probability of 0.9931.

A Study of the Amount of Time It Takes a Mechanic