A Stirling Approach to the Central Limit Theorem (CLT)

Abstract

Many applied statistics courses do not review a proof of the Central Limit Theorem; they rely on simulations like Galton's Quincunx, and/or sampling distributions to acquaint the students with the Bell Curve. the Bell Curve is there, but students are left asking: 1.) where did the pi come from?, 2.) how did a power function based on e get into the formula? the short answer to that question is "Stirling's Formula for n!." Looking at the accuracy of Stirling's Formula can give students some useful insights into the DeMoivre-LaPlace (binomial distribution) version of the Central Limit Theorem (CLT).