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The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that

(a) as we look at more and more bulbs, their average burnout time gets ever closer to the mean $\mathrm{μ}$ for all bulbs of this type.

(b) the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the population distribution.

(c) the average burnout time of a large number of bulbs has a distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.

(d) the average burnout time of a large number of bulbs has a distribution that is close to Normal.

(e) the average burnout time of a large number of bulbs has a distribution that is exactly Normal.

Step by step solution

01

Given Information

The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right.

02

Explanation

According to the central limit theorem, if the sample size of a sampling distribution is $30$ or greater, the sample mean is nearly normal, with a mean of $\mathrm{μ}$ and a standard deviation of $\frac{\mathrm{σ}}{\sqrt{n}}$.

As a result, the average burnout time of a large number of bulbs has a Normal distribution.

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