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 is less than 8.9 hours.

A. 0.9589
B. 0.9756
C. 0.4276
D. 0.9608

Answer 1

To find the probability that the mean rebuild time is less than 8.9 hours, we calculate the z-score and look up the probability in the standard normal distribution table. The correct option is A. 0.9589.

Step-by-step explanation:

To find the probability that the mean rebuild time is less than 8.9 hours, we need to calculate the z-score and then look up the probability in the standard normal distribution table.

The z-score formula is: z = (x - μ) / (σ / √n)

Using the given values, we have z = (8.9 - 8.4) / (1.8 / √40) = 1.6667.

Looking up the z-score of 1.6667 in the standard normal distribution table, we find the probability to be approximately 0.9525.

Therefore, the correct option is A. 0.9589.