Elizabeth Gondek - 10_15_2020 APStats Homework

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Rutgers University *

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Statistics

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Jan 9, 2024

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Name________________________ AP Statistics HOMEWORK ~ Describing Location in a Distribution & Finding Z-scores 1. Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT scores is symmetric and single-peaked, with mean 500 and standard deviation 100. Gerald takes the ACT Mathematics test and scores 27. ACT scores also follow a symmetric, single-peaked distribution - but with mean 18 and standard deviation 6. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score? Show your work to prove your findings. 2. Three landmarks of baseball achievement are Ty Cobb’s batting average of .420 in 1911, Ted Williams’ .406 in 1941, and George Brett’s .390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric, except for outliers such as Cobb, Williams, and Brett. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: DECADE MEAN STANDARD DEVIATION 1910s 0.266 0.0371 1940s 0.267 0.0326 1970s 0.261 0.0317 Compute the standardized batting average for Cobb, Williams, and Brett to compare how far each stood above his peers.

*For #3 and #4, refer to the dot plot and summary statistics of salaries for players on the World Champion 2008 Philadelphia Phillies baseball team. 3. Brad Lidge played a crucial role as the Phillies’ closing pitcher throughout the season. His salary for the 2008 season was $6,350,000. a) Find the percentile corresponding to Lidge’s salary. Explain what this value means. b) Find the z-score corresponding to Lidge’s salary. Explain what this value means. 4. Did Ryan Madson, who was paid $1,400,000, have a high salary or low salary compared with the rest of the team? Justify your answer by calculating and interpreting Madson’s percentile and z-score. 5. Scores on the ACT follow a Normal distribution with mean 18 and standard deviation 6. Wyatt’s standardized score on the ACT was -0.7. What was his actual ACT score? 6. George has a bowling average of 180 and bowls in a league where the average for all bowlers is 150 and standard deviation is 20. Bill’s bowling average is 190 and bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in his own league? George or Bill?

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