Copyright © 2013 Louis M. Houston. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using two measurements, we produce an estimate of the mean and the sample standard deviation. We construct a confidence interval with these parameters and compute the probability of the confidence interval by using the cumulative distribution function and averaging over the parameters. The probability is in the form of an integral that we compare to a computer simulation.