This type of problem has come up twice today, so maybe it will help if I walk through a similar problem.

Let's say a stats class recently took their final. Upon grading the tests, the professor finds that the scores fit a normal distribution. The mean number of questions answered correctly is 125 and the standard deviation is 20 questions. After handing back the tests, one of the students asks what score corresponds with the upper 25%.

I find it helpful to draw the normal curve and then shade in the part under the curve I am trying to find. In this case, you would shade in the right 25% of the curve.

First we need to find the z-score that corresponds with our problem. Since we're concerned with the *top* 25% of the curve, we subtract that from one.

1 - .25 = .75

Now we go to the z-table and look for the closest number to .75 in the body of the table. .7486 is the closest in the z-table I have. Now I look to the row/column headings to find the z-score, which is .67 in this case.

Now I have enough of the equation to solve for x, which is the score we're concerned about.

z = (x - mean)/sd

.67 = (x - 125) / 20

Now for a bit of algebra...

(20).67 = (x - 125)(20) / 20

13.4 = x - 125

125 + 13.4 = x - 125 + 125

138.4 = x

So anyone who got 139 or more of the questions correct placed in the top 25% of the class.