Question

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.a. exactly normal for large sample sizesb. approximately normal for all sample sizesc. exactly normal for all sample sizes

Answer 1

Answer:

Approximately normal for large sample sizes

Step-by-step explanation:

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 $s = \frac{\sigma}{\sqrt{n}}$.

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

In this question:

The distribution is unknown, so the sampling distribution will only be approximately normal when n is at least 30.

So the correct answer should be:

Approximately normal for large sample sizes