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 1.77 hours.
Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the mean times are normally distributed, what percentage of sample means are greater than 7.7 hours?

Question

Quizplus · Accepted Answer

The standard error of the mean is 1.77/sqrt(40). The z-score for 7.7 hours is calculated using the formula (7.7 - 8.4) / (1.77/sqrt(40)). The z-score is approximately -2.67. Using the standard normal distribution table, the percentage of sample means greater than 7.7 hours is about 99.38%.

A Study of the Amount of Time It Takes a Mechanic