Build times part 2

Question

A study of the amount of time it takes to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 9.1 hours and the standard deviation is 1.8 hours. If 75 mechanics are randomly selected, what is the first quartile of the sample mean?

Answer 1

The first quartile is the first 25% of the area under the sample mean normal curve.

P(Z< ((x-9.1)/(1.8/sqrt(75)) = 0.25

InvNorm(0.25, 0,1, LEFT) = -0.6745

Solving for x, where

(x-9.1) / (1.8/sqrt(75)) = -0.6745

x = -0.6745(sqrt(75)/1.8) + 9.1 = 8.96

8.96 is the first quartile of the sample mean