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Use the following information. A standardized math test has a mean score of 200 and a standard deviation of $15 .$ Find and interpret the z-scores of the following math test scores.$$233$$

Intro Stats / AP Statistics

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

Descriptive Statistics

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Lectures

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01:53

Consider a sample with a m…

03:53

A sample has a mean of 120…

00:45

Suppose a normal distribut…

02:55

The test grades for a stan…

01:33

Find the $z$ -score for te…

00:26

A data set has mean 25 and…

02:46

An exam produced grades wi…

00:24

What is the $z$ -score of …

03:37

a. Find the $z$-score for …

00:22

okay, We need to find some Z values. And if you look a couple pages back, they say that Z values you, take the data point, subtract the mean from it and then divided by the standard deviation. They tell us right away the meanness 500 standard deviation is 100. And so I've gone ahead and just plug this in to Google Sheets. Example. I'm gonna walk you through step by step. How I did this on my computer. I took each of one of these subtracted to mean divided by the standard deviation. So let's take a look first I said, OK, take this. Selby, too. And I apologize that that too wasn't there, but this is two and three and four. But anyway, take this cell and subtract 500 and I just clicked enter, and that's exactly what it did. You could do it by hand pretty easily to see that 500 20 minus 500 is 22. Do all these by hand as well. But I just let my calculator do all that work for me. And these are the values I got. Not surprisingly, when we subtract this from 500 Of course, we're going negative because these two are the two values that are below 500. So if you do that Mice 500 Yep. We'll get negative values and 500 miles. 500 0 next. So just kind of rewinding. What we did is subtracted from the mean Now we got divided by the standard deviation. So to do that, all we had to do notice is take each of these cells and say, Hey, divided by 100 for me. And so is this a cell C two again? There's a to here is the three here, take the cell divided by 100. Do that for me five times and I'll get my Z values. And there they are. So that's 200 divided by 100 150. Divide by 100. And not surprisingly, these values look similar to these values, except if we move some decimal points over two spaces. So there they are,

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