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 0.318. 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 = 0.318 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 2016 regular season, Kris Bryant of the Chicago Cubs had 37 games with 3 at-bats. 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.

(a) Based on Pedroia’s and Bryant’s hits in games with 3 at-bats, which player do you think had the higher batting average?

(b) Look up Bryant’s 2016 regular season batting average. Was your expectation from part (a) correct? If not, propose a reason why.

Transcribed Image Text:

Frequency Frequency 20 15 Games with Three At-Bats 15 10 5 5 0 0 + 0 1 2 3 Number of hits Games with Five At-Bats 16 15 14 10 8 5. 4 1 5 0 1 2 3 4 Number of hits Frequency 30 30 20 10 Games with Four At-Bats 30 21 19 3 0 1 2 3. 4 Number of hits