Standard Normal

  • Nick T. Thomopoulos


The normal distribution is perhaps the most used distribution in business, engineering and scientific research and analysis of data. The distribution is fully described by two parameters, the mean and the standard deviation. A related distribution is the standard normal that has a mean of zero and standard deviation equal to one. Almost all statistical books have table measures listed on the standard normal. An easy conversion from the normal variable to the standard normal variable and vice versa is available. Since there is no closed-form solution to the cumulative probability of the standard normal, various approximations have been developed over the years. The Hasting’s approximation is applied here and table listings in the chapter are derived from the same. The standard normal variable ranges between minus and plus infinity, but almost all of the probability falls within minus and plus 3.0. For ease of calculations in the chapter and the book, only the range of the standard normal between minus and plus 3 is used. For an application in a latter chapter, (Bivariate Normal), the standard normal distribution is converted to a discrete distribution, for which the variable changes from continuous to a discrete; and table values of the discrete normal are listed here for later use.


  1. 1.
    Gauss, J. C. F. (1809). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Google Scholar
  2. 2.
    Hastings, C., Jr. (1955). Approximation for digital computers. Princeton: Princeton University Press.Google Scholar
  3. 3.
    Abramowitz, M., & Stegun, I. A. (1964). Handbook of mathematical functions with formulas, graphs and tables (pp. 931–937). Washington, DC: U.S. Department of Commerce.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Nick T. Thomopoulos
    • 1
  1. 1.Stuart School of BusinessIllinois Institute of TechnologyChicagoUSA

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