IMathAS-libretexts

Which of the following statements about the sampling distribution of the sample mean, $\displaystyle \overline{{x}}$ , is not true?

The distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.
The distribution is normal regardless of the sample size, as long as the population distribution is normal.
The distribution's mean is the same as the population mean.
The distribution's standard deviation is smaller than the population standard deviation.
All of the above statements are correct.