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Make the given changes in the indicated examples of this section and then solve the indicated problem. In Example $2,$ what percentage of the test scores are between 350 and 650?

$99.7 \%$

Intro Stats / AP Statistics

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

Descriptive Statistics

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Lectures

0:00

11:23

Test Scores The mean score…

00:50

Write a proportion that c…

02:01

The score $175 / 200$ was …

02:10

use the four-step strategy…

02:41

Solve each percent problem…

07:55

Use the data in exercise 4…

01:18

Find the percent of the to…

01:53

Describe how you could fin…

Consider a sample with a m…

02:42

Assume that the test score…

will come to enumerate in the current problem. We are given that there is a test and the schools of the tests are well distributed with a mean uh musicals to 500 standard division sigma is equals to 50. Now, first, let us understand how the question that asks that what percentage of of the test scores for the students will be very its schools Hi between 3 52 6 50. Now this normal distribution that were observed for years, it was found that this percent 68%. Okay. Lies between forget about the spots. It's free. Okay. No, next mm Incurable contains 95% and the large internal contents 99%. Okay, by that. What do we understood? So if I take the blue pink highlighter this area we see a lot. This is one sigma interval. This contents this is 65% 68% of the entire data. Okay, so this pink highlighted area is a area that contains 68%. Now if we take one more sigma limits then we get this idea. This looks like this could be the total area of 95%. Only 5%. 2.5% here, 2.5% here and 99%. If we think then we have all the way from here to live here. This entire area comes under the 99% percentage or data is constructed by this. Now how will you find this? Right? So for them the first thing that we will do is right down there values over here. So mu is equal to 500. Okay so this center so now if I just crop this image for a better understanding at this moment. Mhm. So what are we going to have? We are going to have 500 over here. So next value 500 plus once it moments 5 50 this value would be 505 50 plus. One more sigma. So 600 this would be 650. Same way. If we step back from 500 this point would be 4 50. This limit will be 400 and this limit will be 350. So what do you think empirically and political relations? Where is how much this is containing? So they provide. So this is 16. Okay, right 95%. But we are still all there. We are from here to here. So from here two here this is 99%. So therefore 3 52 6 50 contains 99% of the entire test course. So I hope you could understand this. Let me know if you have any questions.

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