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 more than 40,000 miles?

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Quizplus · Accepted Answer

The exponential distribution is defined by the rate parameter λ = 1/mean. Here, the mean is 42,000 miles, so λ = 1/42,000. The probability that a tire lasts more than 40,000 miles is given by P(X > 40,000) = e^(-λ * 40,000) = e^(-40,000/42,000) ≈ 0.3858.

Suppose the Average Tread-Life of a Certain Brand of Tire