© Approximations for cumulative distribution function of standard normal Omar M. Eidous * Enas Ananbeh Department of Statistics Faculty of Science Yarmouk University Irbid Jordan Abstract In this paper, Tocher’s approximation for standard normal distribution function is improved and three new approximations are proposed. The quality of the new approximations was computed based on two criteria; the maximum absolute error and the mean absolute error. We found that the maximum absolute errors of the proposed approximations fall between 7 7.62 10 - ´ and 5 4.95 10 - ´ and the mean absolute errors -based on 5001 values between 0 and 5- fall between 7 1.82 10 - ´ and 5 1.59 10 . - ´ Subject Classification: 62E17. Keywords: Normal distribution, Approximations, Cumulative distribution function, Maximum absolute error, Mean absolute error. 1. Introduction The normal distribution is one of the most important continuous distribution functions, where the cumulative distribution function of normal distribution is used in various sciences and fields. If a random variable Z is normally distributed with mean ( 0) m = and standard deviation ( 1) s = then the resulting distribution is known as the standard normal distribution. The probability density function of Z is given by, *E-mail: omarm@yu.edu.jo 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Journal of Statistics & Management Systems ISSN 0972-0510 (Print), ISSN 2169-0014 (Online) DOI : 10.1080/09720510.2021.1892278