Standard Normal Probabilities

The standard normal probabilities table is essential to a host of statistical computations. As you know, that table gives the area under the standard normal curve to the left of a particular z-score.

We also use the table “backwards”: If we know a probability, we can use it to compute a corresponding z-score.

In R, you use pnorm to go from z-score to probability and qnorm to go back again.

> pnorm(0)
[1] 0.5
> pnorm(-1)
[1] 0.1586553
> pnorm(-2)
[1] 0.02275013
> pnorm(-3)
[1] 0.001349898
> pnorm(1)
[1] 0.8413447
> pnorm(2)
[1] 0.9772499
> pnorm(3)
[1] 0.9986501
> qnorm(.50)
[1] 0
> qnorm(.25)
[1] -0.6744898
> qnorm(.10)
[1] -1.281552
> qnorm(.99)
[1] 2.326348