A study of the amount of time it takes a mechanic to rebuild

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 1.77 hours. Assume that a random
sample of 40 mechanics is selected and the mean rebuild time of the
sample is computed. Assuming the mean times are normally distributed,
what percentage of sample means are greater than 7.7 hours?

A. 0.62%

B. 34.46%

C. 65.54%

D. 99.38%

Solution

mean = 8.4

std dev = 1.77

For x = 7.7, z = (7.7 - 8.4) / 1.77 = -0.39

Hence P(x > 7.7) = P(z > -0.39) = [total area] - [area to the left of -0.39]

= 1 - 0.3446 = 0.6554 = 65.54%

hence option c is correct.