OK - so I am working on some statistics homework and I ran across a problem. I know how to calculate the z number and everything but I am having trouble trying to understand when to add the percents and subtract them. For instance, why do I add the 2 percents when I take one that 13 below the mean and 13 above the mean (like 57 and 83 +/- 70 as the mean) and then I subtract the two percents when I am on one side of the mean (like 83 and 93 with the same mean of 70)? Does it have to do with the fact that the first set on both sides the mean are symmetrical, or does it have to do with both numbers being on the same side of the mean?
ok, well here is a link to an online quiz: I understand most everything, but I don’t understand the last two, especially when to add .5 and when to take the percent answer from .5 Also, if I am trying to find the percentage of people in a certain range, say 57-80 with a mean of 70, why do I add the two percents I get from the calculated z number? Why don’t I do the same thing from calculating the percentage of people who fall between 83 and 93 with the same mean of 70? I hope this is better.
What link? In any case, the best way to solve these kinds of problems is to just draw a picture (i.e., a bell curve with the desired probability shaded in), compute the z-values for the relevant points, then look up the relevant probabilities from a table. Whether you add, subtract, subtract from 1, or subtract from .5 will depend on what kind of table you are using. Sometimes the table provides the cumulative probability from the left tail (- infinity) to a z-value, and other times the table provides the cumulative probability from the middle (z=0) to a positive z-value. The approach is obvious when you look at your picture and take into account what kind of table you are using.
In your example where you want the probability between x=83 and x=93 when the mean is 70, first convert x=83 to a z-score (can’t do this for you since I don’t know the standard deviation), then convert x=93 to a z-score. If the table is a cumulative from the left tail, find the probability for the second z-score (the one for x=93) and subtract the probability for the first z-score (the one for x=83).