This article explores the different theoretical assumptions necessary to execute a Traditional Confidence Interval, Nonparametric Bootstrap Confidence Interval, and Parametric Bootstrap Confidence Interval. Throughout this article the same data set is used to demonstrate the procedures in the R programming language so that it can be shown that the three methods produce similar results when the data set happens to have the same known probability distribution. The Cumulative Distribution Function (CDF), the Empirical Cumulative Distribution Function (ECDF), and the Glivenko–Cantelli Theorem are discussed.