Distribution at Number l]l Hits in Baseball Games The official website of Major League Baseball, MLB.com, records detailed statistics about players and games. During the 2016 regular season, Dustin Pedroia of the Boston Red Sox had a batting average of (1.318. The graphs below show the number of hits he had in games in which he had different numbers of at-bats. Frequency 1. Games with Three At-Bats 15 [l l 2 Number of hits Games with Five At-Bats 2 3 4 5 Number of l'lllS Construct a probability distribution for the number of hits in games with (a) 3 at-bats. (b) 4at-bats. (c) 5 at-bats. . Construct binomial probability distributions for p = 0.318 and (a) n = 3, (b) n = 4. and (c) n = 5. . 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. Games with Four Al-Bais -. 30 t... C: i M O I Frequency 5 3 1 {l l 2 3 Number of hits 4. During the 2016 regular season. Kris Bryant of the Chicago Cubs had 37 games with 3 atbats. Of these games. he had 11 games with no hits, 18 games with one hit. 7 games with two hits. and 1 game with three hits. (:1) Based on Pedroia's and Bryant's hits in games with 3 at-bats, which player do you think had the higher batting average? (h) Look up Bryant's 2016 regular season batting average. Was your expectation from part (a) mrrect? If not. propose a reason why Case Study 237