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 we select a sample of 40 tires and use a simulator to determine the tread life. What is the likelihood of finding that the sample mean is between 59,050 and 60,950?
A) 0.4332
B) 0.8664
C) 1.00
D) Very likely

Question

Quizplus · Accepted Answer

We can use the central limit theorem here to approximate the distribution of sample means as normal with a mean of 60,000 and a standard deviation of 4,000/sqrt(40) = 632.46. Then, we can find the z-scores for the lower and upper bounds:

z1 = (59050 - 60000)/632.46 = -1.50
z2 = (60950 - 60000)/632.46 = 1.50

Using a standard normal table or calculator, we can find the probability of the sample mean being between these bounds:

P(-1.50 < z < 1.50) = 0.8664

Therefore, the likelihood of finding that the sample mean is between 59,050 and 60,950 is 0.8664, or choice B.

The Tread Life of Tires Mounted on Light-Duty Trucks Follows