central limit theorem

What is the central limit theorem

The central limit theorem refers to a given Arbitrarily distributed In general . Every time I randomly choose from these populations n Samples , altogether smoke m Time . Then put this m The average value is obtained by group sampling . these The distribution of the mean value is close to the normal distribution . （ therefore , Some questions can be transformed into normal distribution and relevant conclusions can be used ）

significance
The central limit theorem tells us , When the sample size is large enough , Sample mean The distribution of slowly becomes normal , This has nothing to do with the data of the sample population . The core ： Independent homologous distribution A random variable Mean normal distribution of .

Example ：

 

 

Ideas ： The central limit theorem , Explain the mean distribution of this group of data , Showing a normal distribution . According to the binomial distribution , It can be found that its mean value is 20, The standard deviation is 16, The result can be obtained by normalizing the normal distribution .