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 between 57,000 and 63,000 miles?
A) 0.4332
B) 0.8664
C) 1.00
D) Very likely

Question

Quizplus · Accepted Answer

The mean tire life of four tires is calculated as the average of individual tire life. Since the individual tire life follows a normal distribution, the mean tire life also follows a normal distribution with mean 60,000 miles and standard deviation 4,000 miles/sqrt(4) = 2,000 miles. 
Therefore, we need to find the probability that a normal random variable with mean 60,000 and standard deviation 2,000 falls between 57,000 and 63,000. 
Using a standard normal distribution table or calculator, we can calculate this probability as P(-1.5 < Z < 1.5) = 0.8664, where Z is a standard normal random variable. 
Hence, the likelihood that the mean tire life of these four tires is between 57,000 and 63,000 miles is 0.8664 or 86.64%. Therefore, the best choice is B.

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