Normal distribution curve index > area between two z values on opposite sides

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## How to find the area between two z values on opposite sides of the mean

If you want to find the area between two z-scores, the technique will differ slightly depending on if you have two z scores on one side of the mean or on opposite sides of the mean. This article will show you how to find the area between two z scores on opposite sides of the mean. If you have z scores on the same side, see: Area Between Two Z Values on One Side of the Mean.

**Step 1:** *Look in the z-table** for the z-scores by finding the intersections of both scores individually*. For example, you might be asked to find the area between two z values of -0.46 and +1.16, so look up both numbers: 0.46 (see note below about absolute values) and 0.16. The table below shows the z-table value for 0.46 (0.4 in the left hand column and 0.06 in the top row. The intersection = .6772).

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:** *Add the values you found in step 1 together*.

*That’s it!*

*note. Bell curves are symmetrical, so ignore negative z-values and just look up their absolute values. For example, if you want to find the area between two z values of -3 and -4, look up 3 and 4.

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What if you are using z-scores produced with class boundaries in a CHi Square test

Hi, Joe,

Can you post your question on the forum? Unfortunately, I don’t have the time to answer math questions here.

Thanks,

Stephanie

Hi Why did you add “”Area between two z values on opposite sides of mean” How can i tell when to subtract and add? is it when they are in both sides add? and subtract? Thank you

Hi, April,

You add the two values together to get the total area.

Whether you add or subtract doesn’t really have an easy answer. It depends on a lot! For example, sometimes you might need to subtract a lower tail area to get the “upper percentage”. My suggestion would be to always draw a graph, and remember that you are trying to find the area. That way you should be able to tell if you are adding, or subtracting.