# Z-value

#### JeneanW

##### New Member
Hello!
I'm new here. I have a problem that I've been working on for a few hours that I just can't seem to figure out. I decided to work the example in the book, but I'm having a problem determining where to get it and how the z-value is applied. So far I've worked out my bell curve, but don't know where to go from there. Here's the problem.

Professor Mann has determined that the scores in his statistics course are approximately normally distributed with a mean of 72 and a standard deviation of 5. He announces to the class that the top 15 percent of the scores will earn an A. What is the lowest score a student can earn and still receive an A?

The book says - The z-value associated corresponding to 35 percent is about 1.04. Where does this come from???

The formula then becomes 1.04=x-72/5 then
X = 72 + 1.04(5) = 72 + 5.5 = 77.2

I saw the link from another post that displays a z table, but it does not go up to 35, so should my problem go beyond the table is there a formula for figuring the z-value?

#### isingofolaf

##### New Member
Hi There,

I've been working on a few posts this hour, and this one is kind of related to the last one I did.

First, we need to understand some concepts. Suppose you have some data that has a bell curve distribution (like the students' grades). If you have one particular score, say, 95%, you can calculate how much this score "deviates" from the average, this is kind of what the z-score calculates. The z-score equals the number of standard deviations one observation (here 95%) deviates from the mean (here 72%).

When the book says that the z-value associated to 35% is about 1.04, it means that if you measure the area under the bell curve from 0 (where the mean should be) to 1.04, you should get a value of about .35, which means that about 35% of the population got scores within this range.

When you look up values in z-score table, look for .35 in the cells of the table, not on the edges for example, in this table if you look up row 1.0-column0.04, you will see the desired value: .3508. This is how you use the table.

So the formula you worked out:

X = 72 + 1.04(5) = 72 + 5.5 = 77.2

the 77.2% you got means something like, approximately 35 percent of students (remember what z=1.04 means?) will score in the 72-77.2% range.

To answer the problem in the book, consider everything above and ask yourself this question:

If only 15 percent will get an A, at what point (i.e. at what z-score) will 85% (i.e. those not getting an A) of the curve lie to the left of that z-score?

To make life easier, remember that 50% of the students should be to the left of the mean. So, how do you find the other 35% above average students that don't get A's (I think we just answered that question by pointing out the 35% bit). This professor is incredibly lenient!