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 64 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.6 hours

Since we know the population standard deviation and the sample size is above 30, then we use the z statistic. The formula for z score is:

z = (x - u) / s

where,

x = the sample mean or sample value = 8.6 hours

u = the population mean = 8.4 hours

s = the standard deviation = 1.8 hours

Substituting into the given equation:

z = (8.6 - 8.4) / 1.8

z = 1.11

Using the standard probability distribution tables for z, a value of z = 1.11 has a probability of:

p = 0.8665

However this is still not the correct answer since this refers to the left of z. What we are trying to find is to the right of z since problem ask for exceeds 8.6 hours, therefore the correct answer is:

P (x>8.6 hours) = 1 - 0.8665

P (x>8.6 hours) = 0.1335

Therefore there is a 13.35% chance that the mean rebuild time is greater than 8.6 hours.