How to find the area under a normal distribution curve (two tails)
There are a few ways to find the area under a normal distribution curve for both tails 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).
Step 1: Look in the z-table for one of the given z-values by finding the intersection. For example, if you are asked to find the area in the tail to the left of z= -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).
Step 2: Subtract the z-value you just found in step 1 from 0.500. Set this number aside for a moment.
Step 3: Repeat steps 1 and 2 for the other tail.
Step 4: Add both z-values together.
*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.