Two Tailed Normal Curve: How to find the area
A two tailed normal curve is one where there’s an area in each of the two tails. In order to find the area for a two tailed normal curve, all you have to do is know how to read a z-table. Z-tables are just lists of percentages. The total area under a normal distribution curve is 100%(1.) and the z-table lists areas as a fraction of that percentage. For example, you could look up a z-value for 60% of a normal curve (.6) or 6% (0.06).
If you are looking for other variations on finding areas under curves, see the normal distribution curve index). The index lists several variations on area finding under a curve, like finding areas for right-tailed normal curves or left-tailed normal curves.
Two Tailed Normal Curve: How to find the area: Steps
Step 1: Look in the z-table for one of the given z-values by finding the intersection. For example, if you are asked to find the area in the tail to the left of z= -0.46, look up 0.46.* The table below illustrates the result for 0.46 (0.4 in the left hand column and 0.06 in the top row. the intersection is .1772).
Step 2: Subtract the z-value you just found in step 1 from 0.500. In this example, if you found .1772 as your z-value, then 0.500 – .1772 = .3228. Set this number aside for a moment.
Step 3: Repeat steps 1 and 2 for the other tail. For example, you might have symmetrical tails (that’s the most common spread for two-tailed problems). So if you repeat the steps you would get .3228 again.
Step 4: Add both z-values together.In this example, the two z-values are .3228 and .3228, so:
.3228 + .3228 = .6456