老师可否解析下AB不对的具体原因呀

问题如下：

Question If the distribution of the population from which samples of size n are drawn is positively skewed and given that the sample size, n, is large, the sampling distribution of the sample means is most likely to have a:

选项：

A.mean smaller than the mean of the entire population. B.variance equal to that of the entire population. C.distribution that is approximately normal.

解释：

Solution

C is correct. Given a population that has a finite variance and a large sample size, the central limit theorem establishes that the sampling distribution of sample means will be approximately normal, will have a mean equal to the population mean, and will have a variance equal to the population variance divided by the sample size.

A is incorrect. Given a population that has a finite variance and a large sample size, the central limit theorem establishes that the sampling distribution of samples means will have a mean equal to the population mean.

B is incorrect. Given a population that has a finite variance and a large sample size, the central limit theorem establishes that the sampling distribution of sample means will have a variance equal to the population variance divided by the sample size.