To explain:Whether the given statement is correct or not

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Faiza Fuller · Accepted Answer

Given information:
The given statement is,
"if $\overset{―}{x}$ is the mean of a large (n > 30) simple random from a population with mean \mu and standard deviation $σ$ , then $\overset{―}{x}$ is approximately normal with $σ_{\overset{―}{x}} = \frac{σ}{\sqrt{n}}$ .
The central limit theorem is one of the important concepts of the large sample theory.
According to the central limit theorem, for a sufficiently large sample size, the sampling distributions of the mean tend to be normal distribution, irrespective of the distribution of the population.Generally, a sample size more than 30 is considered a large sample.
The sampling distribution of the sample mean bar x for the large samples follows normal distribution with mean and variance $\frac{σ^{2}}{n}$ , where mu is the population mean, n is the sample size and $σ^{2}$ is the population variance, that is,
$\overset{―}{x} s i m N (μ, \frac{σ}{\sqrt{n}})$
$\overset{―}{x} s i m N (μ, σ_{\overset{―}{x}})$
Thus, the provided statement is true.

To explain:Whether the given statement is correct or not

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