215 CASE STUDY Distribution of Number of Hits in Baseball Games Case Study 215 The official website of Major League Baseball, MLB.com, records detailed statistics about players and games. During the 2020 regular season, José Abreu of the Chicago White Sox had a batting average of 0.317. The graphs below show the number of hits he had in games in which he had different numbers of at-bats. EXERCISES 1. Construct a probability distribution for the number of hits in games with (a) 3 at-bats. (b) 4 at-bats. (c) 5 at-bats. 2. Construct binomial probability distributions for p = 0.317 and (a) n = 3, (b) n = 4, and (c) n = 5. 3. Compare your distributions from Exercise 1 and Exercise 2. Is a binomial distribution a good model for determining the numbers of hits in a baseball game for a given number of at-bats? Explain your reasoning and include a discussion of the four conditions for a binomial experiment. 4. During the 2020 regular season, Mookie Betts of the Los Angeles Dodgers had 11 games with 3 at-bats. Of these games, he had 3 games with no hits, 5 games with one hit, and 3 games with two hits. (a) Based on Abreu’s and Betts’s hits in games with three at-bats, which player do you think had the higher batting average? (b) Look up Betts’s 2020 regular season batting average. Was your expectation from part (a) correct? If not, propose a reason why. 2 0 Number of hits 1 2 3 Frequency 6 8 4 10 Games with Three At-Bats 4 2 0 7 2 5 0 Number of hits Frequency 10 20 15 Games with Four At-Bats 1 2 3 3 4 5 2 17 2 0 Number of hits Frequency 4 8 6 10 Games with Five At-Bats 0 1 4 2 9 3 2 0 0 4 5
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