The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the distribution of the population.
Sample sizes equal to or greater than 30 are often considered sufficient to perform CLT.
A key aspect of CLT is that the mean of the sample means and standard deviations will be equal to the population mean and standard deviation.
A sufficiently large sample size can more accurately predict the characteristics of the population.
CLT is useful in finance when analyzing a large set of securities to evaluate portfolio distribution and characteristics of return, risk and correlation.