What is the Central Limit Theorem and how does it relate to the normal distribution?

  • It states that all distributions are ultimately normal distributions
  • It states that the mean of a large sample is always equal to the population mean
  • It states that the sum of a large number of independent and identically distributed random variables tends to be normally distributed
  • It states that the sum of a small number of random variables has an exponential distribution
The Central Limit Theorem states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined (finite) expected value and finite variance, will be approximately normally distributed, regardless of the shape of the original distribution.
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