The Standard Normal Distribution in R

By Joseph Schmuller

Working with the standard normal distribution in R couldn’t be easier. The only change you make to the four norm functions is to not specify a mean and a standard deviation — the defaults are 0 and 1.

Here are some examples:

> dnorm(0)

[1] 0.3989423

> pnorm(0)

[1] 0.5

> qnorm(c(.25,.50,.75))

[1] -0.6744898 0.0000000 0.6744898

> rnorm(5)

[1] -0.4280188 -0.9085506 0.6746574 1.0728058 -1.2646055

This also applies to the tigerstats functions:

> pnormGC(c(-1,0),region="between")

[1] 0.3413447

> qnormGC(.50, region = "below")

[1] 0

To standardize a set of scores so that you can compare them to other sets of scores, you convert each one to a z-score. The formula for converting a score to a z-score (also known as a standard score) is eq08002.