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 can be used to determine the shape of a sampling distribution in which of the following scenarios?
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
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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.