Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. For a set of four tires, what is the probability that the average tire life is between 57,000 and 63,000 miles?
A) 0.4332
B) 0.8664
C) 1.00
D) Very likely

Question

Quizplus · Accepted Answer

To calculate the probability of the average tire life being between 57,000 and 63,000 miles, we need to use the formula for the standard error of the mean:

Standard Error = standard deviation / square root of sample size

Since we have four tires, the sample size is 4, so the standard error is:

Standard Error = 4000 / sqrt(4) = 2000

Next, we can calculate the z-score for each endpoint:

z1 = (57000 - 60000) / 2000 = -1.5
z2 = (63000 - 60000) / 2000 = 1.5

Using a standard normal distribution table or calculator, we can find the area between these two z-scores:

Area = 0.8664

Therefore, the probability that the average tire life is between 57,000 and 63,000 miles is 0.8664. The best choice is B.

Truck Tire Life Is Normally Distributed with a Mean of 60,000