1) In the '08 - '09 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? Show work! 2) Knowing 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 which being 5 below average is not an unusually poor performance. 3) Of 281 MLB players during the 2008 season, Jeff Mathis of the L.A. 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. The mean number of runs scored was 65 with a standard deviation of 23.6. Which performance was worse? Explain your answer. Hint: Show work for 2 z-scores 4) In the 2008 NFL regular season, Kurt Warner of the Arizona Cardinals had an average of 286 passing yards with a standard deviation of 103 yards. If the z-score for a particular game was 1.3, how many yards did he throw for? Show work! @5) Suppose you and your friends decided to start a fantasy basketball league using NBA players. You will keep track of your players' statistics for 4 variables: points, rebounds, assists and turnovers. The table below shows mean and standard deviation for each of these variables from the '08 - '09 regular season. Use methods of this chapter to give these players an overall ranking. Hint: Being above avg. with points, rebounds, assists are good however being above avg. with turnovers is bad Hint: Find 4 z-scores for each player (12 z-scores total) then combine z-scores to get their overall ranking. Points Rebounds Assists Turnovers Dwayne Wade 30.2 5.0 7.5 3.4 Dirk Nowitzki 25.9 8.4 2.4 1.9 Dwight Howard 20.6 13.8 1.4 3.0 Mean 11.1 4.5 2.4 1.5 Standard Deviation 5.8 2.4 2.0 0.7 Work for Wade Work for Nowitzki Work for Howard Show work for overall scores @ Overall score: Overall score Overall score: Ranking: Ranking: Ranking: 6) In the Olympics, participants in the Decathlon compete in 10 different track (timed events) and field (distance) events. In each event, participants are awarded points for each performance and the athlete with the highest point total is the winner. How would you use standardized scores to determine a winner rather than using points? a) Add up the z-scores for all the events. b) Add up the z-scores for the timed events and subtract the z-scores for the distance events. c) Add up the z-scores for the distance events and subtract the z-scores for the timed events. d) Subtract the z-scores for all the events