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3. When do we add the two corresponding areas of the Z-score?
Some standard normal tables give the area BETWEEN a z-score and z= 0. Others give the area between a z-score and z= negative infinity (cumulating up to z-score you’re looking up). You can check which kind of of table you have by looking up any pair of z-scores in which one is negative and one is positive (e.g., -1 and 1, or -2 and 2). If the area given is the same, then your table is of the first kind. If the area given for the positive z-score is greater than for the negative z-score, your table is of the latter kind.
You would add the area for a particular z-score to 0.50 if you have (a) a table of the first kind and (b) a question that asks, for example, what’s the probability of getting a positive z-score equal to or less than one you observed? If the z-score was +1.0, the table would tell you that .3413 of the distribution is between z= +1.0 and z=0. You’d add the half of the distribution below z= 0 to get the correct answer of .8413 of the distribution lies below z= +1.0.
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