1. In 11,105 at-bats in the game after facing Tim Wakefield, hitters had a batting average or 0.265.

a. If we assume that these hitters have an ability of 0.274, explain how to use a graphing calculator to simulate the results of these at-bats.

1.

2.

3.

4.

5.

b. Would it be surprising for these hitters to have a performance as low as 0.265 by random chance? Explain using the results of the simulation.

c. Is there convincing evidence that batters have a lower ability to hit the day after facing Tim Wakefield? Explain.

2. Describe how to use a random numbers generator to simulate the following performances:

a. A basketball player had the ability to make 73% of her free-throws and she takes 8 free-throws in a game.

1.

2.

3.

4.

5.

3. In 2008, the Los Angeles Dodgers acquired Manny Ramirez from the Boston Red Sox in the middle of the season. When he arrived in L.A., he was an instant sensation, both on and off the field. During the remainder of the regular season in L.A., he had 17 homeruns in 187 at-bats; in the playoffs, he had 4 homeruns in 25 at-bats. Based on his playoff performance, many people remarked what a clutch player Manny was.

a. Use an appropriate type of graph to compare these performances. Briefly describe what you see.

b. Assuming his ability to hit home runs is 9.1%, describe how to simulate the 25 at-bats he had in the playoffs.

1.

2.

3.

4.

5.

c. One hundred trials of the simulation from part b were conducted and the number of home runs in 25 at-bats was recorded for each trial. Do the results of the simulation give convincing evidence that Manny was a clutch hitter in the playoffs? Explain.