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.