Question

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

Answer 1

Answer:

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

Answer 2

The answer is 0.5999