ABSTRACT
There are various theorems concerning the approximation of a distribution, usually near its peak, by the normal distribution. Another source of the normal distribution is that the limit of a sum of a large number of random variables is the normal distribution. The lack of rigor between the theory and the application is so large that the rigor of derivation is often misleading. The rule has been applied to so many different situations with such remarkable results that a theoretical basis has been long sought. G. K. Zipf tried to base it on the natural economy of the situation, following the then popular least action, least time, and least work laws that were of great importance in the growing field of mechanics. The normal approximation to bionomial sums is useful mainly for thinking about situations.
