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Make the given changes in the indicated examples of this section and then solve the indicated problem. In Example $3,$ find and interpret the $z$ -score of an achievement test score of 630

$z=2.6$

Intro Stats / AP Statistics

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

Descriptive Statistics

Missouri State University

Oregon State University

Boston College

Lectures

0:00

01:44

Understanding the $z$ nota…

02:27

Consider a sample with dat…

02:20

If $z=x^{2}-x y+3 y^{2}$ a…

04:57

Find the standard score $z…

04:50

6.110 Find the standard sc…

01:53

Consider a sample with a m…

01:20

Find a $z$ -score satisfyi…

00:55

02:46

An exam produced grades wi…

00:54

Find a z-score satisfying …

Welcome to New Marine in the current problem. It is given that the variable follows a normal 500. That is mean mu is 500 sigma is 50. Okay. And we are asked little brit the significance of the the school of the value. That is a particular value of X. We Excellent but what is it what's going on in the school? First student can go back. So it could be uh minus mu by sigma. That is 6 30 minus 500 by 50. That is 130 divided by 50. So this cancels. And we get if we multiply by two inside we get 26 by 10 that is 2.6. So we have to interpret 2.6. Now if we think of our normal distribution standard normal we know it is centered at Mhm. Now next value comes at one sigma distribution differences one two sigma differences to three sigma difference history. The same way over here minus one over here minus two over here minus three. Nothing of the importance this area. This is 65 oh 68 one thing. Okay, entire vista. Mhm. And if we think off this, yeah, this contains 95% of America right? And if you consider the last one, that is the entire thing of it, this contents 99%. So you can understand if I am considering to and then 2.6 would be somewhere nearby too. See? So if I consider this is a pretty rare value because 68% of data would lie between this and ah 95% data would lie between this. So if I think of 2.6 here and here, even that will include a lot of later. That means what the data is more concentrated here. But if you think data, the probability of line between 1 to 2 that is a narrow line. So if you think 2.6 beyond going to 0.6 is pretty less. So probability of the set value would exceed 2.6 is very small. We can find the exact value from the table, but that will be something 010 something. So that value indicates that this is a pretty rare value. Too awkward and that's where it is so far away from the center. If it was a regular value, it would have looked like 0.15 inches nearby. This or 1.2 something like this. So this value over here is very rare to walker and so holds true for 6 36 30 is we're too occurred. So that's the interpretation that we obtain through the standard value.

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