There will be 28 documents to describe the process of the central limit theorem of the specific probability distribution distribution. This is the first case, Normal distribution. Research method: there are five method to verify the central limit theorem on the case of Normal distribution. (1) Verify the Z-score distribution, using the probability distribution simulator. (2) Verify whether the moments are affected by n, using the probability distribution simulator. (3) The first explained method by displaying the relationship of Xn and X1 + ... + Xn-1 (4) The second explained method by displaying the relationship of the front half of (X1, ..., Xn) and the rear half of (X1, ..., Xn) (5) Compare the Z distribution and the Z-score of the sample mean. Since X1, X2, ..., Xn are i.i.d. Normal distribution, the process can be shown by the simulating the distribution of the additive X random variables. However, Normal is Normal as the n increases, not by the central limit theorem. In this case, the outcome of the central limit theorem is just the property of Normal distribution.