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00:07

Z-Scores! Uh, no. Z-Scores! Uh, no we don't just have an accent when we're saying it.

00:14

It really is Z-Scores. All right, so, let's get to zhe problem.

00:19

What are Z-Scores, and where does the catchy name come from?

00:23

The Z in Z-Scores refers to the Z distribution,

00:27

another name for the normal distribution. Distant cousin of the...

00:31

weird distribution. That's because Z-Scores tell us how many standard deviations...

00:37

a data point is above or below an average, when placed on a...

00:43

standard normal curve, or a curve with a mean zero and standard deviation of one. It looks like...

00:49

this. What's useful about these Z-Scores is that we can use our handy-dandy...

00:55

probability Z-Score chart to find the probability under the curve of any specific data point.

01:01

And this is super useful, because we can find the likelihood of a specific data point occurring, just by...

01:07

knowing its Z-Score. But the data we're given sometimes doesn't come from a standard normal distribution,

01:13

which means we have to standardize our data first before we can use our chart. Now here's a formula to...

01:19

help us standardize our data. Z equals the point we're interested in. X - μ,

01:25

the mean, all over the standard deviation. This squiggly line thing here is standard deviation.

01:31

Suppose we had a patient take a reading abilities test.

01:37

The patient scores a 46 on the test, and the mean of the test scores is 52. With a standard...

01:43

deviation of four. Got it? Well, we want to find the percentile of the...

01:49

patient's score. First, we have to standardize the data, and we'd use our little handy-dandy formula...

01:55

and plug in some numbers. We get Z equals 46 minus 52 over 4, which is negative...

02:01

six over four, which is negative three halves, or negative 1.5. A negative...

02:07

Z-Score means our point is left of, or smaller than,

02:11

the mean, while a positive Z-Score means our...

02:14

number is to the right of, or larger than, the mean.

02:17

Well, yeah, we already knew that when we were told that...

02:20

our point was 46 and our mean was 52.

02:23

We figured that out okay. Our Z-Score is negative 1.5, so we can look at our chart, and we see that our...

02:29

percentage is 0.0668, or the 6.68th percentile.

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