Question

Suppose you have two friends who made 25 and 30 on the ACT. What are their z-scores?
Remember for the ACT, the mean was 20.8 and the standard deviation was 4.8.

Answer 1

The z score is equal to the score, minus the average, divided by the standard deviation. So, the z score for 25 would be:
\[\frac{ 25-20.8 }{ 4.8}\]Since the mean is 20.8 and the standard deviation is 4.8

Answer 2

So it would be just .875?

Answer 3

I like to think of the Z score as asking the question "How many standard deviations away?"

Answer 4

Problem is, this whole section has me really lost. I don't really understand the meaning of standard deviation

Answer 5

Well then, let me see if I can give a good explanation of the "Standard normal distribution" or "Bell curve"

Answer 6

Okiay. I know what that is. It's when it's symmetrical, too, right?

Answer 7

So a lot of times in life, we'll want to look at a set of data. Maybe we're interested in the different heights of a big group of people or the different speeds of the cars passing on a freeway or the scores of different students on a test.

Answer 8

A common theme we'll see with data sets like these is that there'll be an average value. It's the most common height or speed or test score or whatever.

Answer 9

Yeah

Answer 10

And the other data values can be higher or lower than that mean, of course, but the further from that average value we get, the less likely it gets that we'll see something actually at that value.

Answer 11

Okay

Answer 12

So for example if the speed limit on the freeway is 60, we'll see A LOT of cars doing about 60. We'll see some cars doing 65 or 55. We'll see fewer cars doing 70 or 50. If we go WAY out from the mean, say 90 mph or 30 mph, it gets REALLY REALLY unlikely that we'll see any cars doing that speed.