Probability and Statistics > Normal Distributions > Area to the Right of a z score

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## How to find the Area to the Right of a z score

There are a few ways to find the area to the right of a z-score *where z is less than the mean*. With any word problem like this, you’ll need to consult the z-table. The z-table gives you the area between points (i.e. the area to the right of a z score). Once you know how to read a z-table, finding the area only takes seconds!

If you are looking for other variations of word problems like this (for example, finding the area for a value between 0 and any z-score, or between two z-scores, see the normal distribution curve index). That index also includes pictures of all the different types of areas under the normal distribution curve to assist you with choosing the right article to guide you through the process.

## How to find the Area to the Right of a z score: Steps

**Step 1:Split your z-value up by decimal places. **For example, 0.46 becomes 0.4 + 0.06.

**Step 2:** *Look in the z-table **for the given z-value. In order to look up a value in the z-table, find the intersection*. The table below shows 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 |

**Step 3:** Add 0.500 to the * z-value you just found in step 2*.

That’s it!

**Note 1**: You’re adding the .500 because that’s the right side of the graph (i.e. 50%)

**Note 2**. Because the graphs are symmetrical, you can ignore the negative z-values and just look up their positive counterparts. For example, if you are finding an area to the right of a z score and the area of a tail on the left is -0.46, just look up 0.46.

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