You will find many tables of the standard normal distribution function (Z distribution function). Recall this distribution is symmetric about 0, and has a variance of 1. The top row and side column of a Z table give you particular values for Z, while the interior of the table lists P(Z <= z*) or P(0 < Z <= z*), the probability that Z is less than or equal to z* (also called a z-score), or the probability that Z is greater than 0 but less than or equal to z*. This is summarized by:

Z <= z* ---------> Probability p

z > z* ---------> Probability 1 - p

You can see that if you are wanting to know how likely is Z to liebelowz*, the answer is p, and if you want to know how likely Z is to lieabovez*, the answer is 1 - p. For example, If z* = 1.76, a Z table yields Z <= z* with probability .9608, which also means P(Z > z*) = 1 - p = .0392. This also applies to tables starting with a z-score of 0, and a p-value of .5, like the following: http://sweb.cz/business.statistics/normal01.jpg. I will discuss the .5 starting value now.

Other tables instead start with z* = 0, and p = 0, so that the entries are values for P(0 < Z < z*). An example of such a table can be seen at http://www.science.mcmaster.ca/psych...e/z-table2.jpg. To find P(Z < z*) using these tables, recall the symmetry of the distribution. We know 1/2 of the values lie below 0, and 1/2 lie above 0. Therefore P(Z <= 0) = .5 = P(Z > 0). Notice P(Z <= z*) = P(Z <= 0) + P(0 < Z <= z*) = .5 + P(0 < Z <= z*). This means that if our table starts with a z-score of 0 and 0 p-value, we must add .5 to any p-value if we are looking for P(Z <= z*). This is why the previous table began with .5 for z* = 0. Again, this is summarized below

Probability

Z < z* ----------> .5 + p

Z > z* ----------> 1 - (.5 + p) = .5 - p

Keep in mind that Z <= z* and Z > z* are complement events, and the sum of their probabilities must be 1. You can use this fact to double check your test answers.

Using z* = 1.76 from above, and a table whose z-score begins at 0, i see that the table lists .4608. Again, this is P(0 < Z < z*) and if you are looking for P(Z <= z*) or P(Z > z*) you will need to adjust via the above listing.

Hope this helps!