Standardized Scores

Topic 8: Standardized Scores and Normal Distributions

CCLS Interpreting Categorical and Quantitative Data standards Summarize, represent, and interpret data on a single count or measurement variable.  Use the mean and standard deviation of the data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments.  Decide whether a specified model is consistent with results from a given data-generating process, eg, using simulation. Technology http://bcs.whfreeman.com/sris/#t_730892____ Appendix C: Using Fathom CW/HW 1, 3, 5, 7, 9, 11 Standardized Scores

Name: ______Date: _____ Probability & Statistics CW/HW #29

Throughout this assignment, round your answers to the nearest hundredth.

1. In the 2008-2009 NBA regular season, LeBron James of the Cleveland Cavaliers averaged 28.4 points per game with a standard deviation of 8.8 points per game.

a. Calculate and interpret the z-score for a game in which he scored 40 points.

b. Calculate and interpret the z-score for a game in which he scored 25 points.

c. If the z-score for a particular game was -1.86, how many points did he score?

2. Knowing that a PERFORMANCE is below average doesn’t tell us how poor it is. Describe a situation in which being 5 below average is an unusually poor PERFORMANCE and a situation in which being 5 below average is a poor PERFORMANCE, but not unusually poor.

3. Of the 281 players with at least 300 plate appearances in the 2008 Major League Baseball season, Jeff Mathis of the Los Angeles Angels had the lowest batting average (0.194) and Brad Wilkerson of the Toronto Blue Jays scored the fewest runs (21). Overall, the mean batting average was 0.272, with a standard deviation of 0.027, and the mean number of runs scored was 65 with a standard deviation of 23.6. Which PERFORMANCE was worse? Explain, using the methods of this chapter. Standardized Scores

4. In 2008, Drew Brees of the New Orleans Saints nearly broke Dan Marino’s record, set in 1984, for most passing yards in a season. Brees has 5069 yards, just shy of Marino’s 5084. Using the top 28 quarterbacks of 1984 (since there were 28 teams), the mean number of yards was 2839 with a standard deviation of 927. The mean number of yards for the top 32 quarterbacks in 2008 was 3132 with a standard deviation of 886. Who had the better PERFORMANCE, Marino or Brees? Explain your reasoning.