Statistics How To

Area under a curve (between 0 and any z-score)

Normal distribution curve index > Find the area under a curve (between 0 and any z-score)

This article covers finding the area under a curve in statistics. If you’re looking for how to find the area under a curve in calculus, see this other article: How to Find the Area Under the Curve using a Riemann Sum

How to find the area under a curve (between 0 and any z-score)

Finding the area under a curve in statistics is no harder than reading a table. The first step in figuring out the area is to draw a sketch. Why? Because you have seven possibilities for finding the area, like finding the area in a left tail, right tail or between two tails. If you aren’t exactly sure that you’re finding the area right of the mean (between 0 and a z-score), hop over to the Normal distribution curve index), where you’ll find pictures of each of the seven possibilities.

You can look up numbers in the z-table, like 0.92 or 1.32. The values you get from the table give you percentages for the area under a curve in decimal form. For example, a table value of .6700 is are area of 67%.

Note on using the table: In order to look up a z-score in the table, you have to split up your z-value at the tenths place. For example, to look up 1.32 you would look up 1.3 and then look at .02. See the example below for a visual on what finding the intersection looks like.

area under a curve

Normal Distribution curve

Step 1: Look in the z-table for the given z-score by finding the intersection. For example, if you are asked to find the area between 0 and 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

That’s it!

*Note. Because the graphs are symmetrical, you can ignore the negative z-scores and just look up their positive counterparts. For example, if you are asked for the area of 0 to -0.46, just look up 0.46.

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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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Area under a curve (between 0 and any z-score) was last modified: October 12th, 2017 by Stephanie

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