A study 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%

Answer: 43%