In the statistics of large samples, the sample average is a constant times the sum of the random variables in the sampling process . Thus, for large samples, the sample average is approximately normal...In the statistics of large samples, the sample average is a constant times the sum of the random variables in the sampling process . Thus, for large samples, the sample average is approximately normal—whether or not the population distribution is normal. In the case of sample average, the “closeness” to a limit is expressed in terms of the probability that the observed value \(X_n (\omega)\) should lie close the the value \(X(\omega)\) of the limiting random variable.
