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.

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