Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 710806, 8 pages
http://dx.doi.org/10.5402/2012/710806
Research Article

The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

The Louisiana Accelerator Center, The University of Louisiana at Lafayette, Lafayette, LA 70504-4210, USA

Received 5 November 2012; Accepted 25 November 2012

Academic Editors: M.-H. Hsu and X. Liu

Copyright © 2012 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

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.