Question

The number of hours a battery lasts before failing varies from battery to battery. The distribution of Failure times Fallows an Exponential distribution, which is strongly skewed to the right. the central limit theorem says that:_________.

A) as we look at more and more batteries, their average failure time gets ever closer to mean for all batteries of this type.
B) the average failure time of a large number of batteries has a distribution of the same shape (strongly skewed) as the distribution for individual batteries.
C) the average failure time of a large number of batteries has a distribution that is close to Normal.

Answer 1

C) the average failure time of a large number of batteries has a distribution that is close to Normal.

Explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Distribution is skewed to the right.

However, for large samples of batteries, the sampling distribution of sample means will be approximately normal, which means that the answer is given by option c.