How to find the area under the normal distribution curve (between 0 and any z-score)

Critical Values and Z-Tables, Mean Mode Median, Normal Distribution, Standard Deviation 7 Comments

There are a few ways to find the area under a normal distribution curve between 0 and any z-score using a z-table. Once you know how to read the table, finding the area only takes seconds!

If you are looking for other variations (finding the area for one tail, or between two z-scores, see this normal distribution curve index).

Normal_example_graph (1)

Normal Distribution curve

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.

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7 Responses to “How to find the area under the normal distribution curve (between 0 and any z-score)”

  1. How to Do Everything Statistics » Area Under a Normal Distribution Curve Index said:

    Aug 31, 09 at 3:17 pm

    [...] How to find the area under the normal distribution curve (between 0 and any z-value) [...]

  2. Cathy said:

    Sep 06, 09 at 5:27 pm

    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?

  3. Lauren Schultz said:

    Sep 28, 09 at 1:27 pm

    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.

  4. Rebecca Gamble said:

    Oct 01, 09 at 1:41 pm

    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″?

  5. Stephanie said:

    Oct 04, 09 at 8:20 am

    Yes, you are absolutely correct,
    Stephanie

  6. Donna Allen said:

    Oct 07, 09 at 4:20 pm

    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.

  7. Catherine Flanagan said:

    Oct 07, 09 at 6:16 pm

    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?