Question

Solve the problem. 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 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.

Answer 1

= 8.4 hours

= 1.8 hours

n = 40

Sample size > 30. So, according to Central Limit Theorem, the sampling distribution of mean will be normally distributed.

P( < A) = P(Z < (A - )/)

= = 8.4 hours

=

=

= 0.2846

P(mean rebuild time exceeds 7.7 hours) = P( > 7.7)

= 1 - P( < 7.7)

= 1 - P(Z < (7.7 - 8.4)/0.2846)

= 1 - P(Z < -2.46)

= 1 - 0.0069

= 0.9931