Is the statement below true or false? The distribution of the sample mean, x overbar, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.

Using the Central Limit Theorem, it is found that the statement is True.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

In the context of this problem, the sample size restriction is only for non-normal underlying distribution, hence the statement is True.

A similar problem is given at link

Step-by-step explanation:

Given statement is " The distribution of the sample mean, x overbar, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size".

∴ The given statement is true.

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