Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find...
-
Upload
ashley-fitzpatrick -
Category
Documents
-
view
218 -
download
0
Transcript of Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find...
![Page 1: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/1.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Objectives
• Use z-scores to find percentiles.
• Thinking Skill: Explicitly assess information and draw conclusions
12.6 Normal Distributions
![Page 2: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/2.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Glossary Terms
normal curve
normal distribution
standard normal curve
z-score
12.6 Normal Distributions
![Page 3: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/3.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
• Symmetric about the mean, x .
Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• Total area under the curve is 1.
• Mean, median, and mode are about equal.
![Page 4: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/4.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
![Page 5: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/5.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 68% of the area is within 1 standard deviation of the mean.
![Page 6: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/6.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 95% of the area is within 2 standard deviations of the mean.
![Page 7: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/7.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Rules and Properties
Properties of Normal Distributions
12.6 Normal Distributions
• About 99.8% of the area is within 3 standard deviations of the mean.
![Page 8: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/8.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Translation of data values into standard scores• The z-score is a standard score.
• z-score is the number of ______________ ____________ a score is from the __________
• Formula for z-score:
![Page 9: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/9.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Rules and Properties
z-Score
12.6 Normal Distributions
normal distribution
standard deviation:
mean: x
x - x
z =
any data value: x
![Page 10: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/10.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
• Questions on your homework?
![Page 11: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/11.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Percentiles
• The area under the entire curve is one or 100% of the scores
• So area up to a score is the percentile for that score – the percent of scores lower than that score
![Page 12: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/12.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Try this:
• Standardized test scores are normally distributed with a mean of 100 and a standard deviation of 10.
• What percent scored less than 95?
![Page 13: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/13.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Indicate on the drawing what we are looking for.
Find the z-score
Can’t tell % using the Empirical rule.
![Page 14: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/14.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
This table gives the percents for any given z-score
![Page 15: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/15.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
• The z-score for a score of 95 is -.5
• The table shows that the percent of scores lower than a z-score of -.5 is 30.85%
![Page 16: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/16.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
Try some more:
• What is the percent below 120?
![Page 17: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/17.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
• What is the percent higher than 112? (be careful!!)
![Page 18: Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use z-scores to find percentiles. Thinking Skill: Explicitly assess information.](https://reader033.fdocuments.net/reader033/viewer/2022061305/55143c825503462d4e8b46fe/html5/thumbnails/18.jpg)
Copyright © by Holt, Rinehart and Winston. All
Rights Reserved.
• What is the percent scoring between 90 and 115?