Question

Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?

Short answer

The sampling distribution of the sample mean is often approximated using the normal distribution.

Step-by-step solution

Step 1. Introduction

For a variable x and a given sample size, the distribution of the variable $\overline{x}$is called the sampling distribution of a sample mean.

It is the distribution of all possible sample means for samples of a given size.

Step 2. Explanation

Generally, the value of sampling distribution of a sample mean is not known exactly.

But the value can be often approximated by a normal distribution.

That is under certain conditions, the variable $\overline{x}$is approximately normally distributed.