If 40 mechanics are randomly selected, find the probability that their mean rebuild time between 8.1 and 8.6 hours

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier normally distributed and has the mean 8.4 hours and the standard deviation 1.8 hours.

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It is found that the time taken by a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier is normally distributed and has a mean of 8.4 hours and standard deviation of 1.8 hours.

If 40 mechanics are randomly selected the probability that their mean rebuild time is between 8.1 and 8.6 has to be determined.

First determine the z-scores. The formula to be used here is `(x - mu)/(sigma/sqrt N)`

For 8.1, the z-score is: `(8.1 - 8.4)/(1.8/sqrt 40) = -1.054`

For 8.6 it is: `(8.6 - 8.4)/(1.8/sqrt 40) = 0.7027`

Using a standard distribution table the area enclosed by the estimated z-scores is 0.76424 - 0.14686 = 0.6173

**There is a 61.73% probability that the mean rebuild time lies between 8.1 and 8.6**

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