How to find the area between two z values on opposite sides of the mean
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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 (0.4 in the left hand column and 0.06 in the top row. The intersection = .6772).
Step 2: Add the values you found in step 1 together.
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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.
Stephanie Glen. "Area Between Two Z Values on Opposite Sides of Mean" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/area-between-two-z-values/
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