Probability and Statistics > Normal Distributions > How to find area left of a z score

## How to find area left of a z score

You can find area to the left of a z score (where z is greater than the mean) by using a **z-table**. The trick to using a z-table is knowing that the numbers in a z-table represent percentages. For example, a value in the table of 0.5000 represents 50% of the area under the curve and a value of .9999 represents 99% of the area under a curve. Once you know how to read the table, finding the area only takes a step or two!

If you are looking for other variations on area, see the index article, area under a normal distribution curve. You’ll find several articles for all different possibilities of areas. For example, finding the area for a value between 0 and any z-score, or an area to the right of a z-score.

## How to find area left of a z score: Steps

**Step 1: **Split your given decimal into two by decimal places. For example, if you’re given 0.46, split that into 0.4 + 0.06.

**Step 2: ** *Look up your decimals from Step 1 in the z-table*. The z-table below gives the result from looking up 0.4 in the left column and 0.06 in the top row. The intersection (i.e. the area under the curve) 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*.

**Note**: You’re adding .500 because that’s the 50% of the graph between the mean at zero and the far left of the graph. The above steps only gave you the sliver between 0 and the z-score.

*That’s it!*

*note on How to find area left of a z score with negative values. The bell curve is symmetrical, so if you are given negative values you can just look up their absolute values. For example, if you are asked for the area of a tail on the left to -0.96, look up the absolute value of -0.96 (0.96).

------------------------------------------------------------------------------**Need help with a homework or test question?** With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. If you'd rather get 1:1 study help, Chegg Tutors offers 30 minutes of **free tutoring** to new users, so you can try them out before committing to a subscription.

If you prefer an **online interactive environment** to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

**Comments? Need to post a correction?** Please post a comment on our *Facebook page*.

Check out our updated Privacy policy and Cookie Policy