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

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.