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).

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.

Why is the mean .6772 when in the green box it says .1772? Is this because in the top row it is in the 6 column?

This chart is a god-sent item. For those of us, myself included who were a little foggy on the topic right off the bat this will, and did, help me alot.

I’m glad someone already asked the same question that I need help on, but also, just for clarification… “.46” is “.4” on the right and “.06” on the top? And that works if I had “.57” the interception or area would be “.2157”?

Yes, you are absolutely correct,

Stephanie

Your explanation of how to use the Z-table makes it so easy to find the area under the normal distribution curve. Thanks to this clear explanation, this homework assignment has not been overwhelming.

Your explanation was much more helpful than mathzone or the text book. But just curious, if the graph is not symmetrical would you have to find the negative value?

Excellent method to understand such topic.