The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 52,500 miles?
A) 0.0062
B) 0.9938
C) 0.0000
D) 1.0000

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected tire will have a life of at least 52,500 miles, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (52,500 miles), $\mu$ is the mean (40,000 miles), and $\sigma$ is the standard deviation (5,000 miles). Plugging in the values, we get $Z = \frac{52,500 - 40,000}{5,000} = 2.5$. Looking up 2.5 in the Z-table gives us the area to the left of Z, which is approximately 0.9938. Since we want the area to the right (the probability of having a life of at least 52,500 miles), we subtract this value from 1, resulting in $1 - 0.9938 = 0.0062$.

The Life Expectancy of a Particular Brand of Tire Is