Approximations to the Normal DistributionFunction and An Extended Table for the MeanRange of the Normal Variables

This article presents a formula and a series for approximatingthe normal distribution function. Over the whole range ofthe normal variable z, the proposed formula has the greatest absoluteerror less than 6.5e - 09, and series has a very high accuracy. Weexamine the accuracy of our proposed formula and series for variousvalues of z s. In the sense of accuracy, our formula and series are superiorto other formulae and series available in the literature. Basedon the proposed formula an extended table for the mean range of thenormal variables is established