Statistics How To

Two Tailed Normal Curve: How to find the area

Probability and Statistics > Normal Distributions > Two Tailed Normal Curve

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 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 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

two tailed normal curve

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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Two Tailed Normal Curve: How to find the area was last modified: November 10th, 2016 by Stephanie

5 thoughts on “Two Tailed Normal Curve: How to find the area

  1. Sarah Joyner

    These problems were a bit intimidating at first. However going over it a couple times and understanding the table finally, it became really easy to solve these types of problems.

  2. Vanessa DuBarry

    I am still having problems reading these tables.where do I know it intersects? because in the above problem it says its.6772, where did that com from?. and where would I find if the number was 0.72? I dont see it in the table.. please help me asap

  3. Tasnim

    Sir please let me know how do i use ‘Area of the left or right (one tail)’ or ‘Area of the left and right (two tail) to find value of z.

  4. Andale

    It depends on what you are trying to test. If you are looking for > or < a certain value then that is a one-tailed test. If you are looking for both, that's a two-tailed test.

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