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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I’m a little confused how do you get “.6772” from the .4 and .06? Do we just replace the “.1772” in the chart with the 6 category?

The link for the ” look in the z-table” doesn’t link to anything?

Now these prolbem are become earier to do. Except in step two tell to add the 0.500 to the number that we have found. I end up having to substact 0.500 to get the correct answer. So is step two type O or is that the correct way to find that answer.

Mark,

You definitely have to add if your problem looks like the one in the picture, because you are finding the area left of the mean and then adding .5 for the area above the mean. I’m not sure what problem you are working on–if you could let me know what question you are working on, perhaps I could sort out the confusion.

Stephanie

Broken link, now fixed. Thanks for spotting it,

Stephanie

You add .5 to the .1772 in the chart (see step 2),

Stephanie

I found it easier to use the tab that says tables on the top of the screen.

Hi stephanie,

what if the Z value is 1.35 ? How do we determine if Z is less than or bigger than ? I don’t seem to get it ? Is your book explains statistics in an even better way than what is on the website or is it the same ? cause too much explanations and writing examples without going through them step by step with demonstrations is actually confusing.

Thanks

Moe,

You’d still add .500 to your area. If the z score is 1.35, you would have: .4115 + .500 = .9115.

I’m not understanding what you mean by “How do we determine if Z is less than or bigger than ?”. Could you explain that a different way (maybe by giving a sample question you’re working on).

The book is very, very similar to the website content. A few points are explained a little differently, but it’s essentially the same.

very good teaching!!!

Hi Stephanie,

Sorry – this may be the first of many queries as just discovered your site & it’s great.

First query for this one – we know that the right-side of the curve = 0.5 (which is why we add this on).

So why is the table shown using the z-table for the right of the curve? (i.e. (i.e. shouldn’t it be using the z-table for the left of the curve & be 0.6772?)

Thanks!

The z-table is a mirror(the area between 0 and say, .2 would be the same as 0 and -.2). As the left table gives you the area between negative infinity and a z-value, you can’t use that. You have to use the right z table, to give you a value between 0 and any z-score (positive or negative)