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.
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).
*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.