1. Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.4, Slide 1 14 Descriptive Statistics What a Data Set Tells Us

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 14.4, Slide 2 The Normal Distribution 14.4 Understand the basic properties of the normal curve. Relate the area under a normal curve to z -scores. Make conversions between raw scores and z -scores. Use the normal distribution to solve applied problems.

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 3 The Normal Distribution The normal distribution describes many real-life data sets. The histogram shown gives an idea of the shape of a normal distribution.

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 4 The Normal Distribution

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 5 The Normal Distribution We represent the mean by μ and the standard deviation by σ.

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 6 Example: Suppose that the distribution of scores of 1,000 students who take a standardized intelligence test is a normal distribution. If the distribution’s mean is 450 and its standard deviation is 25, The Normal Distribution (continued on next slide) a) how many scores do we expect to fall between 425 and 475? b) how many scores do we expect to fall above 500?

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 7 Solution (a): 425 and 475 are each 1 standard deviation from the mean. Approximately 68% of the scores lie within 1 standard deviation of the mean. We expect about 0.68 × 1,000 = 680 scores are in the range 425 to 475. The Normal Distribution (continued on next slide)

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 14.4, Slide 8 Solution (b): We know 5% of the scores lie more than 2 standard deviations above or below the mean, so we expect to have 0.05 ÷ 2 = 0.025 of the scores to be The Normal Distribution above 500. Multiplying by 1,000, we can expect that 0.025 * 1,000 = 25 scores to be above 500.