There are a few ways to find the area under a normal distribution curve for two z-scores on opposite sides 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 on the same side, see this normal distribution curve index).
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= +0.16, look up both 0.46* and 0.16. The table below illustrates the result for 0.46 (0.4 in the left hand colum and 0.06 in the top row. the intersection is .6772).
Step 2: Add both of the values you found in step 1 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.