 # Two Tailed Normal Curve: How to Find The Area

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## 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, you have to read a z-table.

Watch the video for an example:

Z-tables are lists of percentages. The total area under a normal curve is 100%(1.) and the z-table lists areas as a fraction of that percentage. For example, you could look up a z-score 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 area under a normal distribution curve index. The index lists several variations, like finding areas for right-tailed normal curves or left-tailed normal curves.

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## Two Tailed Normal Curve: How to find the area: Steps area under a normal distribution curve--two tails

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).

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224

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

That’s it!

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## References

Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics, Cambridge University Press.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

CITE THIS AS:
Stephanie Glen. "Two Tailed Normal Curve: How to Find The Area" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/two-tailed-normal-curve/
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