Question

the average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. a lot contains 200 of these vehicles, brand new. 1. how many of the 200 would you expect to fail in their first 2 years?

Answer 1

Of the 200, 44 failures during the first two years are to be expected.

Given;

A specific kind of vehicle has an exponential lifespan that is typically 8 years long. There are 200 of these new cars on a lot.

The probability of failure in the first 2 years is first computed here as:

P(T < 2) for  X = exp(1/8) as for exponential distribution, the parameter is the reciprocal of the mean. Therefore, now using the CDF for the exponential distribution, we get here;

⇒ 1 - $e^\frac{-2}{8}$ = 0.2212

Therefore, 0.2212 is the probability here.

Now the expected number which fails in the first 2 years here is computed as;

⇒ 200 * 0.2212 = 44.24 is the required expected value here.

Hence, 44 of the 200 would you expect to fail in their first 2 years.

To learn more about probability click here:

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