What is the most significant aspect of the central limit theorem?

**Solution: **One thing we know about a distribution is that the population mean represents

something like the “average” of the values the random will take. Also we know that the

standard deviation gives us a measure of how concentrated are the values around the

mean (the smaller the standard deviation is, the more concentrated the values are around

the mean). But unless we know what distribution we have, we cannot really tell the how

the random variable behaves. The central limit theorem indicates that if _{}represents the

sample mean, then _{}converges to a standard normal distribution. This means that

if _{}is big enough, _{}has a normal distribution. In other words, a great deal of regularity

appears when we consider a large sample. Even though the values of the population are

normally distributed, but the average _{}will be approximately normal is _{}is big. This

result is extremely helpful in practical situations.

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