Chapter 13 Section 7 – Slide 1 Copyright © 2009 Pearson Education, Inc. AND

Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 7 – Slide 2 Chapter 13 Statistics

Chapter 13 Section 7 – Slide 3 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Sampling techniques Misuses of statistics Frequency distributions Histograms, frequency polygons, stem-and-leaf displays Mode, median, mean, and midrange Percentiles and quartiles

Chapter 13 Section 7 – Slide 4 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN Range and standard deviation z-scores and the normal distribution Correlation and regression

Copyright © 2009 Pearson Education, Inc. Chapter 13 Section 7 – Slide 5 Section 7 The Normal Curve

Chapter 13 Section 7 – Slide 6 Copyright © 2009 Pearson Education, Inc. Types of Distributions Rectangular Distribution J-shaped distribution

Chapter 13 Section 7 – Slide 7 Copyright © 2009 Pearson Education, Inc. Types of Distributions (continued) Bimodal Skewed to right

Chapter 13 Section 7 – Slide 8 Copyright © 2009 Pearson Education, Inc. Types of Distributions (continued) Skewed to left Normal

Chapter 13 Section 7 – Slide 9 Copyright © 2009 Pearson Education, Inc. Properties of a Normal Distribution The graph of a normal distribution is called the normal curve. The normal curve is bell shaped and symmetric about the mean. In a normal distribution, the mean, median, and mode all have the same value and all occur at the center of the distribution.

Chapter 13 Section 7 – Slide 10 Copyright © 2009 Pearson Education, Inc. Empirical Rule Approximately 68% of all the data lie within one standard deviation of the mean (in both directions). Approximately 95% of all the data lie within two standard deviations of the mean (in both directions). Approximately 99.7% of all the data lie within three standard deviations of the mean (in both directions).

Chapter 13 Section 7 – Slide 11 Copyright © 2009 Pearson Education, Inc. z-Scores z-scores determine how far, in terms of standard deviations, a given score is from the mean of the distribution.

Chapter 13 Section 7 – Slide 12 Copyright © 2009 Pearson Education, Inc. Example: z-scores A normal distribution has a mean of 50 and a standard deviation of 5. Find z-scores for the following values. a) 55 b) 60c) 43 a) A score of 55 is one standard deviation above the mean.

Chapter 13 Section 7 – Slide 13 Copyright © 2009 Pearson Education, Inc. Example: z-scores (continued) b) A score of 60 is 2 standard deviations above the mean. c) A score of 43 is 1.4 standard deviations below the mean.

Chapter 13 Section 7 – Slide 14 Copyright © 2009 Pearson Education, Inc. To Find the Percent of Data Between any Two Values 1. Draw a diagram of the normal curve, indicating the area or percent to be determined. 2.Use the formula to convert the given values to z-scores. Indicate these z- scores on the diagram. 3. Look up the percent that corresponds to each z-score in Table 13.7.

Chapter 13 Section 7 – Slide 15 Copyright © 2009 Pearson Education, Inc. To Find the Percent of Data Between any Two Values (continued) 4. a) When finding the percent of data to the left of a negative z-score, use Table 13.7(a). b) When finding the percent of data to the left of a positive z-score, use Table 13.7(b). c) When finding the percent of data to the right of a z-score, subtract the percent of data to the left of that z-score from 100%. d) When finding the percent of data between two z-scores, subtract the smaller percent from the larger percent.

Chapter 13 Section 7 – Slide 16 Copyright © 2009 Pearson Education, Inc. Example Assume that the waiting times for customers at a popular restaurant before being seated for lunch are normally distributed with a mean of 12 minutes and a standard deviation of 3 min. a)Find the percent of customers who wait for at least 12 minutes before being seated. b)Find the percent of customers who wait between 9 and 18 minutes before being seated. c)Find the percent of customers who wait at least 17 minutes before being seated. d)Find the percent of customers who wait less than 8 minutes before being seated.

Chapter 13 Section 7 – Slide 17 Copyright © 2009 Pearson Education, Inc. Solution a. wait for at least 12 minutes Since 12 minutes is the mean, half, or 50% of customers wait at least 12 min before being seated. b. between 9 and 18 minutes Use table 13.7 on pages in the 8 th edition. 97.7% % = 81.8%

Chapter 13 Section 7 – Slide 18 Copyright © 2009 Pearson Education, Inc. Solution (continued) c. at least 17 min Use table 13.7(b) page % % = 4.7% Thus, 4.7% of customers wait at least 17 minutes. d. less than 8 min Use table 13.7(a) page 889. Thus, 9.2% of customers wait less than 8 minutes.