Main > Definitions > What is a z table

## What is a Z Table: Overview

The **z-table** is short for the Standard Normal Z-Table. The Standard Normal distribution is used in hypothesis testing, including tests on proportions and on the difference between two means. The area under the whole of a normal curve is 1, or 100 percent. The z-table helps by telling us what percentage is under the curve at any particular point.

## What is a Z Table: Standard Normal Probability

Every set of data has a different set of values. For example, heights of people might range from eighteen inches to eight feet and weights can range from one pound (for a preemie) to five hundred pounds or more. Those wide ranges make it difficult to analyze data, so we “standardize” the normal curve, setting it to have a mean of zero and a standard deviation of one. When the curve is standardized, we can use a Z Table to find percentages under the curve.

## Percentages under the curve

## The z-table

Obviously a graph can only give us so much information. The above graph can tell us the area under the curve for one (z= -1 to 1), two (z= -2 to 2) and three (z= -3 to 3) standard deviations from the mean. But what about if we want to know the area between z=-0.78 and z=0.78? Or z=-1.2 and z=0.44? That’s where the z-table comes in. It tells us the area under the standard normal curve for any value between the mean, zero and any z-value.

## Why Are There Two z-tables?

Simply, it’s to make life easier. Sometimes you’ll want to know the area between the mean (0) and some positive value. That’s when you’ll use the regular z-table (area to the right of z). But other times you might want to know the area in a left tail. If that’s the case, use the z-table that shows the area to the left of z.

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