Question

The top-selling Red and Voss tire is rated 50,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 67,000 miles and a standard deviation of 5,200 miles. What is the probability that a tire wears out before 60,000 miles?

Answer 1

Answer: 0.9726

Explanation:

Let x be the random variable that represents the distance the tires can run until they wear out.

Given : The top-selling Red and Voss tire is rated 50,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a
`\mu=`67,000 miles and a
`\sigma=` 5,200 miles.

Then , the probability that a tire wears out before 60,000 miles :

`P(x<60000)=P((x-\mu)/(\sigma)<(60000-50000)/(5200))\\\\=P(z<1.92)=0.9726` [using p-value table for z]

Hence, the probability that a tire wears out before 60,000 miles= 0.9726