The tread life of a particular brand of tire is a random variable best described by a normal distribution with amean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a particular tire of thisbrand will last longer than 57,100 miles?
A) 0.8413
B) 0.1587
C) 0.2266
D) 0.7266

Question

Quizplus · Accepted Answer

To find the probability that the tire will last longer than 57,100 miles, we calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value in question (57,100 miles), μ is the mean (60,000 miles), and σ is the standard deviation (2,900 miles). Plugging in the values, we get Z = (57,100 - 60,000) / 2900 = -2.9 / 2.9 = -1. This corresponds to a probability of 0.8413 to the right of the Z-score in the standard normal distribution table.

The Tread Life of a Particular Brand of Tire Is