The tread life of tires mounted on light duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is more than 66,000 miles?
A) 0.0013
B) 0.9987
C) 0.4987
D) 0.9544

Question

Quizplus · Accepted Answer

We need to use the Central Limit Theorem to approximate the distribution of the sample mean.

The sample mean follows a normal distribution with a mean of 60,000 and a standard deviation of 2,000 (since we are dividing the standard deviation by the square root of the sample size, which is 4 for 4 tires).

Using the standard normal distribution, we can find the z-score for a mean tire life of 66,000 miles:

z = (66000 - 60000)/2000 = 3

Now we need to find the probability of getting a z-score of 3 or more. This can be found from a normal distribution table or calculator:

P(z > 3) = 0.0013

Therefore, the likelihood of the mean tire life of these four tires being more than 66,000 miles is 0.0013.

The Tread Life of Tires Mounted on Light Duty Trucks