A Simple Approximation to the Area under Standard Normal Curve

Abstract

Of all statistical distributions, the standard normal is perhaps the most popular and widely used. Its use often involves computing the area under its probability curve. Unlike many other statistical distributions, there is no closed form theoretical expression for this area in case of the normal distribution. Consequently it has to be approximated. While there are a number of highly complex but accurate algorithms, some simple ones have also been proposed in literature. Even though the simple ones may not be very accurate, they are nevertheless useful as accuracy has to be gauged vis-à-vis simplicity. In this short paper, we present another simple approximation formula to the cumulative distribution function of standard normal distribution. This new formula is fairly good when judged vis-à-vis its simplicity.