# Area Under a Normal Distribution Curve Index

Critical Values > Area Under a Normal Distribution Curve

## How To Find the Area Under a Normal Distribution Curve

How you find the area under a normal distribution curve depends on what your shaded area looks like. Before you can solve for the area under a normal distribution curve, you must be able to imagine what you area looks like. The best (albeit optional) way to imagine this is to make a sketch. For example, let’s say you were give a z-score and were asked to find the area between that score and z=0 (the mean). Your sketch might look like this:

Find an area under a curve from z=0 to z=?

There are seven ways your sketch could look, depending on what values you were given. Once you have drawn your sketch, look at the pictures below. Click on the image that looks like your sketch. the link will take you to a step-by-step guide on how to find the area under a normal distribution curve for that shape. Many of these also have short videos showing the steps.

## Choose One

Find an area under a curve from z=0 to z=?

Find an area in one tailed distribution (left or right)

area between two z scores on same side

area between two z values on opposite sides of mean

area left of a z score (z is greater than the mean)

area to the right of a z score (z is greater than the mean)

area under a two tailed normal curve

Tip: Drawing sketches in probability and statistics isn’t just limited to normal distribution curves. If you get used to making a sketch, you’ll also have an easier time with creating complicated graphs (like contingency tables).

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