Z Values from Integrals over the Normal Probability Density Function
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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
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Reference
[1] J. Steimel, Instrumentation and Experimentation, University of the Pacific. (Feb 23, 2020) scholarlycommons.pacific.edu/open-textbooks/13.
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