Tails of Distributions
Nathan Mantel · The American Statistician · 1976
then for large X, Q(X) may be approximated by Z(X)!X. This approximation is demonstrated in Feller [1957, p. 166] and was first brought to my attention in coursework with Girshick approximately in 1940. Over the years I have been identifying this approximation with a special characteristic of the normal distribution governing average values of normal variables over intervals, as say X1 to X2. The average value over the interval (see derivation in Mantel and Greenhouse, 1967) in terms of the respective densities, Z1 and Z2, and tail areas, Q1 and Q2, is given by