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jek_recluse [69]
3 years ago
11

Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probabil

ity distribution. What is the probability that a randomly selected tire will have a tread-life of less than 65,000 miles
Mathematics
1 answer:
Ahat [919]3 years ago
8 0

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

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

P(X\leq x)=1-e^{\frac{-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^{\frac{-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 .

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