1. 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

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms normal curve normal distribution standard normal curve z-score 12.6 Normal Distributions

3. 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.

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

5. Rules and Properties Properties of Normal Distributions 12.6 Normal Distributions About 68% of the area is within 1 standard deviation of the mean.

6. 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.

7. 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.

8. 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:

9. 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

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Questions on your homework?

11. 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

12. 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?

13. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Indicate on the drawing what we are looking for. Find the z-score Cant tell % using the Empirical rule.

14. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. This table gives the percents for any given z-score

15. 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%

16. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Try some more: What is the percent below 120?

17. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. What is the percent higher than 112? (be careful!!)

18. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. What is the percent scoring between 90 and 115?