How to find the area of a normal distribution between two z-scores on one side of the mean

critical values and z-tables, Normal Distribution 4 Comments

There are a few ways to find the area under a normal distribution curve for two z-scores on one side of the mean 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 a value between 0 and any z-score, or between two z-scores, see this normal distribution curve index).

normal distribution z values on same side

normal distribution -- two z scores on same side

Step 1: Look in the z-table for the given z-scores (you should have two) by finding the intersections. For example, if you are asked to find the area from z= -0.46 to z= -0.40, look up both 0.40 and 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

Step 2: Subtract the smaller  z-value you just found in step 1 from the larger value.

That’s it!

*note. Because the graphs are symmetrical, you can ignore the negative z-values and just look up their positive counterparts. For example, if you are asked for the area of a tail on the left to -0.46, just look up 0.46.

Related posts:

  1. How to find the area under the normal distribution curve between two z-scores on opposite sides of the mean
  2. How to find the area under the normal distribution curve (between 0 and any z-score)
  3. How to find the area under a normal distribution (in any tail)
  4. How to find the area under a normal distribution curve (left of a z-score)
  5. How to find the area under a normal distribution curve (two tails)
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4 Responses to “How to find the area of a normal distribution between two z-scores on one side of the mean”

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

    Sep 01, 09 at 5:51 am

    [...] How to Do Everything Statistics » How to find the area of a normal distribution between two z-… September 1st, 2009 at 5:49 am [...]

  2. Lisa Barcomb said:

    Oct 11, 09 at 8:22 pm

    I understand this really well I like the Z and T tables they are really useful. And you can understand what you are doing when you have problems dealing with these tables, now this is easy. I wish all the problems were like this.

  3. surya prakash rai said:

    Oct 21, 09 at 3:21 am

    i did not get the point that the point of intersection is at 0.1772 but you are saying that it is intersecting at 0.6772.Please help me at this point

  4. Stephanie said:

    Oct 21, 09 at 5:07 am

    Aargh! A typo. Whoops. That’s fixed now. Thanks for pointing it out,
    Stephanie

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