Question

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, find the probability that their mean rebuild time exceeds 8.7 hours.

0.1346

0.1285

0.1946

0.1469

Answer 1

0.1469

Explanation:

Given from the question;

Mean=8.4 hrs=μ

Standard deviation=1.8 hrs=δ

Sample size, n=40

Let x=8.7

z=(x-μ)÷(δ÷√n)

Find z(8.7)

z=(8.7-8.4)÷(1.8÷√40)

z={0.3×√40}÷1.8=1.05409

z=1.0541

Read from the standard normal probabilities table

P(z>1.0541)

=0.1459