Question

Adolis Garcia of the Texas Rangers is a career .243 batter. In a recent season he got at least one hit in 109 of the 157 games in which he played. His longest hitting streak was 23 games, one of the the longest streaks in MLB that season. How much longer was that hitting streak than what would be typical for a player with those statistics? Is it: 9 games longer 12 games longer 17 games longer 19 games longer

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To estimate how much longer Adolis Garcia's hitting streak was than what would be typical for a player with his hitting statistics, we can follow these steps:

1. Calculate the game hitting rate:

\text{Game Hitting Rate} = \frac{109}{157} \approx 0.694

2. Find the probability of the streak ending (not getting a hit in a game):

\text{Probability of not getting a hit} = 1 - 0.694 = 0.306

3. Calculate the expected hitting streak length using the geometric distribution formula:

\text{Expected Streak Length} = \frac{1}{0.306} \approx 3.27 \text{ games}

4. Compare the expected streak length to Garcia's actual 23-game hitting streak:

23 - 3.27 = 19.73

Therefore, Adolis Garcia's hitting streak was approximately 19.73 games longer than what would be typical for a player with his hitting statistics.

\boxed{19.73}

1. Calculate the game hitting rate:

2. Find the probability of the streak ending (not getting a hit in a game):

3. Calculate the expected hitting streak length using the geometric distribution formula:

4. Compare the expected streak length to Garcia's actual 23-game hitting streak:

Therefore, Adolis Garcia's hitting streak was approximately 19.73 games longer than what would be typical for a player with his hitting statistics.

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