Astudy 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, ? nd the probability that their mean rebuild time exceeds 8.7 hours

Given:
μ = 8.4 hours, the population mean
σ = 1.8 hours, the population std. deviation

The random variable to be tested is x = 8.7 hours
A sample size of 40 (> 30) is large enough for testing against the normal distribution.

Calculate the z-score.
z = (x - μ)/σ = (8.7 - 8.4)/1.8 = 0.1667

From standard table, obtain
P(x <= 8.7) = 0.5662
Therefore
P(x>8.7) = 1 - 0.5662 = 0.4338 or 43%

 43%