Statistics Definitions > Inverse Normal Distribution

## What is an Inverse Normal Distribution?

An inverse normal distribution is a way to work backwards from a known probability to find an x-value. It is an informal term and doesn’t refer to a particular probability distribution.

**Note**: the Inverse Gaussian Distribution and Inverse Normal Distribution are often confused. See this comment at the end of the article for clarification.

## How to Find Inverse Normal on the TI-83 with the InvNorm Command

The InvNorm function (Inverse Normal Probability Distribution Function) on the TI-83 gives you an x-value if you input the area (probability region) to the left of the x-value. The area must be between 0 and 1. You must also input the mean and standard deviation.

**Sample question**: Find the 90th percentile for a normal distribution with a mean of 70 and a standard deviation of 4.5.

Step 1: Press 2nd then VARS to access the DISTR menu.

Step 2: Arrow down to 3:invNorm( and press ENTER.

Step 3: Type the area, mean and standard deviation in the following format:

**invNorm (probability,mean,standard deviation).**

For this example, your input will look like this:

**invNorm(90,70,4,.5).**

The x-value (90th percentile) is 75.767.

## What is the Difference Between Inverse Normal Distribution and Inverse Gaussian Distribution?

The names “Gaussian Distribution” and “Normal Distribution” mean the same thing (i.e. a bell shaped curve). Physicists use the term Gaussian and Statisticians use the term “Normal.” However, **The inverse normal distribution is not the same thing as the Inverse Gaussian distribution**. The inverse normal distribution refers to the technique of working backwards to find x-values. In other words, you’re finding the inverse. The inverse Gaussian is a two-parameter family of continuous probability distributions. The “inverse” in “inverse Gaussian” is misleading because the distribution i*sn’t actually an inverse*. In fact, at large values of it’s shape parameter, **the inverse Gaussian looks exactly like the normal distribution.**

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