Solve the problem.
-A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 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 8.1 hours.
A)0.8531
B)0.9146
C)0.7285
D)0.8457

Question

Quizplus · Accepted Answer

To find the probability that the mean rebuild time exceeds 8.1 hours for a sample of 40 mechanics, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{8.1 - 8.4}{1.8/\sqrt{40}} = \frac{-0.3}{1.8/\sqrt{40}} \approx -1.41$. Looking up -1.41 on the z-table gives us the probability of being below this value, so we subtract this from 1 to find the probability of exceeding 8.1 hours. This gives us approximately 0.8531, indicating that there's an 85.31% chance the mean rebuild time exceeds 8.1 hours for a sample of 40 mechanics.

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