The central limit theorem states that the mean of a sufficiently large number of iterates of independent random variables, each with well-defined mean and well-defined variance, will be approximately distributed. This is the definition in the probability theory.
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The Central Limit THeorem say that the sampling distribution of .. is ... It would help if you read your question before posting it.
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
Yes, the theorum still has merit.
Binomial Theorum
James A. Garfield
The central limit theorem basically states that as the sample size gets large enough, the sampling distribution becomes more normal regardless of the population distribution.