# Area Between Two Z Values on Opposite Sides of Mean

## How to find the area between two z values on opposite sides of the mean

Watch this video showing the steps to finding the area between two z values on opposite sides:

If you want to find the area between two z-scores, the technique will differ slightly depending on if you have two z-scores on one side of the mean or on opposite sides of the mean. This article will show you how to find the area between two z-scores on opposite sides of the mean. If you have z-scores on the same side, see: Area Between Two Z Values on One Side of the Mean.

Step 1: Look in the z-table for the z-scores by finding the intersections of both scores individually. For example, you might be asked to find the area between two z values of -0.46 and +1.16, so look up both numbers: 0.46 (see note below about absolute values) and 0.16. The table below shows the z-table value for 0.46 Â (0.4 in the left hand column and 0.06 in the top row. The intersection = .6772).

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: Add the values you found in step 1 together.

That’s it!

*note. Bell curves are symmetrical, so ignore negative z-values and just look up their absolute values. For example, if you want to find the area between two z values of -3 and -4, look up 3 and 4.

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## References

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. New York: Wiley, 1968.
Patel, J. K. and Read, C. B. Handbook of the Normal Distribution. New York: Dekker, 1982.
Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 285-290, 1999.