Z Values from Integrals over the Normal Probability Density Function

z

1

1.7

z

2

-0.35

In this Demonstration, we compute integrals over the normal probability density function between two values,

z

1

and

z

2

. Each

z

-score represents the number of standard deviations away from the mean, defined as

(x-μ)/σ

, where

x

is some value or measure,

μ

is the population mean and

σ

is the standard deviation. When integrating between two values of

z

, 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

z

limits of

z

1

=1

and

z

2

=2

. This would give a probability of approximately 13.6% for finding a sample between these

z

bounds.

References

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

Permanent Citation

Ethan Hall, Michael Pappas, Joshua Paul Steimel

"Z Values from Integrals over the Normal Probability Density Function"
http://demonstrations.wolfram.com/ZValuesFromIntegralsOverTheNormalProbabilityDensityFunction/
Wolfram Demonstrations Project
Published: February 26, 2021