# Z Values from Integrals over the Normal Probability Density Function

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

In this Demonstration, we compute integrals over the normal probability density function between two values, and . Each -score represents the number of standard deviations away from the mean, defined as , where is some value or measure, is the population mean and is the standard deviation. When integrating between two values of , the integral gives the probability or confidence interval for a measurement between these two values. For example, given a sample of tensile specimens with a population mean length of 1m and a standard deviation of 0.1m, the probability of finding a sample between 1.1m and 1.2m can be found by integrating between limits of and . This would give a probability of approximately 13.6% for finding a sample between these bounds.

Contributed by: Ethan Hall, Michael Pappas and Joshua Paul Steimel (May 2021)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Reference

[1] J. Steimel, *Instrumentation and Experimentation*, University of the Pacific. (Feb 23, 2020) scholarlycommons.pacific.edu/open-textbooks/13.

## Permanent Citation