# Important information about Central Limit Theorem

What evidence do we have that the Central Limit Theorem is true? Why do so many of life's events share the same characteristics with Central Limit Theorem? How would you demonstrate the Central Limit Theorem to your classmates?

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#### Solution Preview

(1) Central limit theorem is a direct mathematical result of the Taylor's expansion of exponential functions and the law of large numbers. Therefore, I would consider the most direct evidence that the Central Limit Theorem is true would be the mathematical proof (please see attachment). One of the real life evidence for the Central Limit Theorem is to toss a fair coin a number of time (what else can you expect in Statistics class?) and record the number of heads. Repeat the entire process and plot the result ...

#### Solution Summary

The central limit theorem proof is examined.