Question

Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life of less than 65,000 miles

Answer 1

Answer: The probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .

Explanation:

The cumulative distribution function for exponential distribution is :-

`P(X\leq x)=1-e^{(-x)/(\lambda)}`, where
`\lambda` is the mean of the distribution.

As per given , we have

Average tread-life of a certain brand of tire :
`\lambda=\text{42,000 miles }`

Now , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles will be :

`P(X\leq 65000)=1-e^{(-65000)/(42000)}\\\\=1-e^(-1.54761)\\\\=1-0.212755853158\\\\=0.787244146842\approx0.7872`

Hence , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .