What is the Central Limit Theorem and why is it important for sampling distributions?

  • It guarantees that large samples are always normally distributed
  • It says that the sample mean equals the population mean
  • It states that every statistic has a normal distribution
  • It states that the sampling distribution of a mean will approach normality as the sample size increases
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that the sampling distribution of a mean will approach normality as the sample size increases, regardless of the shape of the population distribution. The importance of CLT is that it enables us to make statistical inferences about the population mean based on the properties of the normal distribution.
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