中心极限定理

问题如下：

Which of the following statements about the sampling distribution of a sample mean is correct?

选项：

A.

The sampling distribution is the probability distribution including all datas that population including.

B.

The sampling distribution is the probability distribution including all possible sample means calculated from samples whose size is different.

C.

The sampling distribution is the probability distribution including all possible sample means calculated from samples whose size is the same.

解释：

C is correct.

Assume a population includes 500 members. If we select 50 menbers ten times, than distribution of ten sample means form an sampling distribution.

样本均值的抽样分布是所有的相同size的样本均值形成的分布，即μ的概率分布。

样本均值的抽样分布在形状上是对称的。随着样本量n的增大，不论原来的总体是否服从正态分布，样本均值的抽样分布都将趋于正态分布，其分布的数学期望为总体均值μ，方差为总体方差的1/n。这就是中心极限定理（central limit theorem）