# Sampling from a normally distributed population.

What can we conclude when sampling from a normally distributed population? In other words, what can we conclude about samples drawn from a normally distributed population with mean equal to μ and standard deviation equal to σ ?

The followings hold true:

a.

The mean of x̄ or μ is equal to the mean of the population or μ.

μx̄ = μ

The standard deviation of x̄ or σ is equal to σ/√n assuming of course n/N ≤ 0.05

$$\sigma_{\overline{x}} = \frac{\sigma }{\sqrt{n} }$$

b. No matter what the value of n is, the shape of the sampling distribution of x̄ is also normally distributed.

## Recent Articles

1. ### What is Statistics? Definition and Examples

Aug 16, 22 04:10 AM

What is statistics? The word statistics can mean two different things. First, it may refer to numerical facts ...

## Check out some of our top basic mathematics lessons.

Formula for percentage

Math skills assessment

Compatible numbers

Surface area of ​​a cube