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The test grades for a standardized test are normally distributed with a mean of $50 .$ A gradeof 60 represents a z-score of $1.25 .$ What is the standard deviation of the data?

$\sigma = 8$

Intro Stats / AP Statistics

Chapter 15

STATISTICS

Section 6

Normal Distribution

Sampling and Data

The Normal Distribution

Linear Regression and Correlation

Missouri State University

Piedmont College

University of St. Thomas

Boston College

Lectures

0:00

00:35

A data set has mean 25 and…

02:35

A sample has a mean of 50 …

00:45

Suppose a normal distribut…

05:52

An instructor gives a 100-…

03:53

A sample has a mean of 120…

A set of 250 data values i…

01:33

Find the $z$ -score for te…

00:26

00:22

01:53

Consider a sample with a m…

08:18

Using the standard normal …

00:23

In a normal distribution, …

00:37

00:18

What is the z-score of $x=…

03:22

a. Find the $z$-score for …

11:23

Test Scores The mean score…

00:46

A set of values has a mean…

04:42

Find the probability that …

03:28

a. Find the standard $z$-s…

02:46

An exam produced grades wi…

All right, This is a Z score question. So have gone ahead and written out the formula for Z score. The way you find a Z score, Jersey score is equal to your data value minus you mean divided by the standard deviation. I wrote it out What they actually mean. And then I did write the symbols over here. So the blue X just represents, you know, just basic X. Whatever your data value is, X with the line over, it represents the mean That's the statistical representation for a mean and then on the denominator. That is a lower case, Sigma. It's a Greek letter and lower case Sigma represents the standard deviation in this case. All right, so the problem that we're given tells us that we have a Z score of 1.25 tells us our grade, meaning our data value is 60. And it tells us that we have a mean of 50 and then it asks us, What would the standard deviation for that be? So we use that liver case signal just like the book does for standard deviation. Okay, So while this is Aziz core question, now that we've plug stuff into the formula. The rest of this is really just basic algebra of that. We have an equation. We need to solve it out for the variable. Okay, so first thing I would do I see I have a 60 minus 50 up there. I'm gonna go ahead and combined those. So I've got one. Whoops. Forgot to change colors. So I've got 1.25 equals 60 minus 50 is 10 divided by signal. All right, So if I want to get Sigma by itself, that's the goal. First things first. My issues signals in the denominator. I'm not trying to solve for one over signem trying to solve for signal. So I need to get that signal out of the denominator. Uh, opposite of division. There's multiplication as we know. So I would say best option here would be to multiply by Sigma on both sides so that we can get it out of the denominator, will slow in changing colors here, apologised. So that would cancel out the signal here that would leave us with 1.25 times. Sigma is equal to 10. Well, now that I've got 1.25 times the signal. I'm trying to get by itself. The opposite of multiplication is division. So I simply just need to divide 1.25 to the other side. And I should have my answer. If you take 10 divided by 1.25 you should get that Sigma is equal to eight. So eight is our standard deviation in this scenario.

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