The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2100 miles. What is the
Probability a particular tire of this brand will last longer than 57,900 miles?
A).2266
B).1587
C).8413
D).7266

Question

Quizplus · Accepted Answer

To find the probability that a tire will last longer than 57,900 miles, we calculate the Z-score and then find the corresponding probability from the standard normal distribution. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (57,900 miles), $\mu$ is the mean (60,000 miles), and $\sigma$ is the standard deviation (2,100 miles). Plugging in the values, we get $Z = \frac{57,900 - 60,000}{2,100} = -1$. Looking up the Z-score of -1 in the standard normal distribution table or using a calculator, we find that the area to the left of Z = -1 is approximately 0.1587. Since we are interested in the probability of lasting longer than 57,900 miles, we subtract this value from 1 to get the probability to the right of Z = -1, which is 1 - 0.1587 = 0.8413.

The Tread Life of a Particular Brand of Tire Is