EXPLANATION OF PROCEDURE USED WITH Z-TABLE NUMBER 2.

You want to enter a z-score entry of -2. This would give you the area to the left of a z-score of -2 which would be equal to .022750 (left picture).

You can't do this, however, because TABLE 2 does not provide z-scores less than 0.

You enter a z-score entry of 2 instead. This give you a z-table entry of .977250 which is the area to the left of a z-score entry of 2 (middle picture).

You subtract the z-table entry of .977250 from 1 to get .022750 which is the area to the right of a z-score of 2 (right picture). Since this is exactly equal to the area to the left of a z-score of -2, you take this value and use it for the area to the left of a z-score of -2 (left picture).

The area to the right of the z-score entry of 2 is exactly the same as the area to the left of the z-score entry of -2. This applies to all z-scores. The area to the left of a z-score that is negative is always equal to the area to the right of the same z-score that is positive. This is why the procedure used for z-table number 2 works.