Finding Scores from Z score table

#1
Scores on the WAIS test approximate a normal curve with a mean of 100 and a standard deviation of 15.

Q: What IQ score is identified with the upper 60 percent?

Hi, I'm am unclear how to calculate the upper 60%. I recognize that with the upper 60% we are dealing 50% to the right and 10% below the mean to the left. I want to use column 3 due to the fact that we are not calculating anything between the Mean to Z, but I don't know how to go about this.

0.500 or the 50% right of the mean would give a Z score of 0, and I don't know how to figure out the Z score for the 10% to the left of the mean. Thanks for the help!

NKA
 
#3
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.
 
#6
I've seen z-tables done two ways. The one I used for the problem includes the 50% lower half under the curve. So, .5 + .2486 = .7486. Your table starts at the mean of the normal distribution, and is probably the most common and preferred table. (I accidentally picked up my non-preferred stats book.) My textbook displays a drawing of the normal curve under the table with the portion the table refers to shaded in.

Your table is probably the better table to use, and I should have used it since I'm trying to find the portion of the distribution equal to and greater than a certain score. So the logic goes like this:

I want to find the upper 25% of the scores, so I look for the percentage closest to 25% in the body of the z-table. Then I take that z-score (still .67) and solve for x.

Does that make sense? I apologize for the confusion...