Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. What is the probability that a tire lasts between 54,000 and 66,000 miles?
A) 0.4332
B) 0.8664
C) 1.00
D) Very likely

Question

Quizplus · Accepted Answer

To find the probability that a tire lasts between 54,000 and 66,000 miles, we need to find the z-scores for each value and then use a z-table to find the area under the normal curve between those z-scores.

z-score for 54,000 miles: (54,000 - 60,000) / 4,000 = -1.5
z-score for 66,000 miles: (66,000 - 60,000) / 4,000 = 1.5

Using a standard normal distribution table or a calculator with built-in normal distribution functions, we can find the area under the curve between these two z-scores to be approximately 0.8664. This means that there is a 86.64% chance that a randomly selected tire will last between 54,000 and 66,000 miles. Therefore, the best choice is B (0.8664).

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