a study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 chevrolet colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. if 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours. round to four decimal place

The answer is 0.9599.

Explanation:

mu (sample) = mu = 8.4

s.d. (sample) = 1.8/ sq. rt. 40

P( greater than 8.1) = (8.9-8.4)/(1.8/ sq. rt. 40)

Let x be the mean time for the 40 mechanics

Standardize the mechanics: (8.9-8.4)/(1.8/ sq. rt. 40) = 1.75 = Z

P( x > 8.9) = P(Z > 1.75), this means the area to the right of Z = 1.75.

Then you need to look in the table of the Normal distribution, Z(1.75) =0.9599