Sample Size and the
Central Limit Theorem

We know that as the sample size becomes larger, the sample mean comes closer to approaching the true Mean.  However we have also stated that it is necessary to use samples of an 'acceptable' size.  To determine what is acceptable we must rely on that most powerful of factors, general consensus.  It is common practice to consider the arbitrary sample size of 30 as the minimun acceptable value for n .

However, if the original population itself is normally distributed, then the sample means will be normally distributed regardless of the sample size n .