The term **inverse normal distribution** refers to the method of using a known probability to find the corresponding z-critical value in a normal distribution.

This is not to be confused with the Inverse Gaussian distribution, which is a continuous probability distribution.

This tutorial provides several examples of how to use the inverse normal distribution in different statistical softwares.

**Inverse Normal Distribution on a TI-83 or TI-84 Calculator**

You’re most likely to encounter the term “inverse normal distribution” on a TI-83 or TI-84 calculator, which uses the following function to find the z-critical value that corresponds to a certain probability:

**invNorm(probability, μ, σ)**

where:

**probability:**the significance level**μ:**population mean**σ:**population standard deviation

You can access this function on a TI-84 calculator by pressing 2nd and then pressing vars. This will take you to a **DISTR **screen where you can then use **invNorm()**:

For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:

The z-critical value that corresponds to a probability value of 0.05 is **-1.64485**.

**Inverse Normal Distribution in Excel**

To find the z-critical value associated with a certain probability value in Excel, we can use the **INVNORM()** function, which uses the following syntax:

**INVNORM(p, mean, sd)**

where:

**p:**the significance level**mean:**population mean**sd:**population standard deviation

For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:

The z-critical value that corresponds to a probability value of 0.05 is **-1.64485**.

**Inverse Normal Distribution in R**

To find the z-critical value associated with a certain probability value in R, we can use the qnorm() function, which uses the following syntax:

**qnorm(p, mean, sd)**

where:

**p:**the significance level**mean:**population mean**sd:**population standard deviation

For example, we can use this function to find the z-critical value that corresponds to a probability value of 0.05:

qnorm(p=.05, mean=0, sd=1) [1] -1.644854

Once again, the z-critical value that corresponds to a probability value of 0.05 is **-1.64485**.