1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1

2. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 6 The Standard Deviation as a Ruler and the Normal Model

3. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 3 Finding Normal Percentiles Using Technology Many calculators and statistics programs have the ability to find normal percentiles for us. Using the TI-83 to Compute Probabilities on the Normal Curve Using the TI-83 to Compute Probabilities on the Normal Curve

4. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 4 Finding Normal Percentiles Using Technology What is the probability of an observation between 0 and 1.34 in the normal curve where the mean is 0 and the standard deviation is 1? What is the probability of an observation less than z=1.34 in the normal curve where the mean is 0 and the standard deviation is 1? Find the probability that an observation falls between 0 and.78 where the mean is.5 and the standard deviation is 1.

5. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 5 Finding Normal Percentiles Using Technology Find the probability that an observation falls above -1.62 where the mean is 2 and the standard deviation is 3. Consider a normal distribution where the mean is 56.8 and the standard deviation is 5.5. What is the probability of an observation between 60 and 70? Consider a normal distribution where the mean is 10 and the standard deviation is 15. What is the probability of an observation larger than 20?

6. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 6 From Percentiles to Scores: z in Reverse Sometimes we start with areas and need to find the corresponding z-score or even the original data value. Example: What z-score represents the first quartile in a Normal model where the mean is 0 and the standard deviation is 1?

7. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 7 From Percentiles to Scores: z in Reverse Consider a normal distribution where the mean is 55 and the standard deviation is 15. What is the 63rd percentile? What is the 12th percentile? Scores on a particular test follow a normal distribution with a mean of 75.6 and a standard deviation of 7.8. Find the score separating the top 15% of the scores from the bottom 85% of scores.