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 mechanicsare randomly selected, find the probability that their mean rebuild time exceeds 9.1 hours.
A) 0.1046
B) 0.0069
C) 0.0046
D) 0.1285

Question

Quizplus · Accepted Answer

The probability can be found using the standard normal distribution. First, calculate the standard error (SE) using the formula SE = σ/√n = 1.8/√40. Then, find the z-score for 9.1 hours using the formula z = (X̄ - μ) / SE. Finally, use the z-score to find the probability from the standard normal distribution table. The probability that the mean exceeds 9.1 hours corresponds to choice B.

A Study of the Amount of Time It Takes a Mechanic