Statistics How To

One tailed distribution (How to find the area)

Probability and Statistics Index > Critical Values > One Tailed Distribution

One tailed distribution (How to find the area)

A one-tailed distribution in statistics refers to a shaded area in one tail of a probability distribution.

one tailed distribution

Normal Distribution curve with left tail shaded

There are a few ways to find the area under a one tailed distribution curve. The easiest, by far, is looking up the value in a z-table. A z-table gives you percentages, which represent the area under a curve. For example, a table value of 0.5000 is 50% of the area and 0.2000 is 20% of the area.

If you are looking for other other area problems, see the normal distribution curve index. The index lists seven possible types of area, including two tailed, one tailed, and areas to the left and right of z.

Note: In order to use a z-table, you need to split your z-value up into decimal places (i.e., tenths and hundredths). For example, if you are asked to find the area in a one tailed distribution with a z-value of 0.21, split this into tenths (0.2) and hundredths (0.01).

One tailed distribution (How to find the area): Steps

Watch the video or read the steps below:

Step 1: Look up your z-score in the z-table. Looking up the value means finding the intersection of your two decimals (see note above). For example, if you are asked to find the area in a one tailed distribution to the left of z= -0.46, look up 0.46 in the table (note: ignore negative values. If you have a negative value, use its absolute value). The table below shows that the value in the intersection for 0.46 is .1772. This figure was obtained by looking up 0.4 in the left hand column and 0.06 in the top row.

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: Take the area you just found in step 2 and add .500. That’s because the area in the right-hand z-table is the area between the mean and the z-score. You want the entire area up to that point, so:
.5000 + .1772 = .6772.

Step 3: Subtract from 1 to get the tail area:
1 – .6772 = 0.3228.

That’s it!


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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One tailed distribution (How to find the area) was last modified: October 12th, 2017 by Stephanie

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