A Sojourn with Numerical Approximations to the Normal Distribution Suitable for the Undergraduate Classroom

Abstract

Several transcendental approximations to the Normal Distribution are contrasted relative to mean absolute as well as maximum absolute error. Low degree Lagrange and Chebyshev polynomial interpolants are similarly studied to reduce mathematical complexity. Ultimately, a piecewise polynomial approximation, easily understood and handy for students, is explored as an alternative. This approximation is amenable to simple programming on a graphing calculator. Classroom examples are proposed and discussed.