Which of the following statements about the sampling distribution of the mean $($distribution of sample means$)$ and the central limit theorem $($CLT$)$ are true?

Select four $(4)$ true statements from the list below:

The sampling distribution is always approximately normal even if the population is not normal.

If the population is normally distributed, then sample size does not matter for the central limit theorem to apply.

The sampling distribution is still assumed to be approximately normal if the underlying population is negatively skewed as long as the population is large.

If a population is perfectly normal, then for the distribution of sample means of any size, ${}_{\stackrel{}{x}}=$ and ${}_{\stackrel{}{x}}=.$

The sampling distribution of the mean will be approximately normal when $n$ is large.

From the same population, the standard error of the sampling distribution with $n=12$ will be larger than the standard error with $n=37.$

From the same population, the mean of the sampling distribution $({}_{\stackrel{}{x}})$ with $n=7$ will be smaller than the mean with $n=12.$

The larger the sample size, the smaller the standard error.

If ${}_{\stackrel{}{x}}=$ and ${}_{\stackrel{}{x}}=\frac{}{\sqrt[\phantom{2}]{n}},$ then the distribution of sample means is normal.

The larger the sample size, the smaller the difference between the mean of the sampling distribution and the population mean.

axc

Suningy