In the 2014 MLB season the Los Angeles Dodgers won 94 games and lost 68 to finish in first place in the National League Western Division. Over the 162 games of the regular season they scored an average of 4.43 runs per game, with a standard deviation of 2.88 runs per game. The distribution of their 162 run PERFORMANCES is roughly symmetric, unimodal, and bell-shaped. Dodger Stadium. Photo credit losangeles.dodgers.mlb.com Sketch what this distribution should look like by drawing a bell-shaped curve and labeling the mean, mean ± 1 SD, mean ± 2 SD, and mean + 3 SD.
In the 2014 MLB season the Los Angeles Dodgers won 94 games and lost 68 to finish in first place in the National League Western Division. Over the 162 games of the regular season they scored an average of 4.43 runs per game, with a standard deviation of 2.88 runs per game. The distribution of their 162 run PERFORMANCES is roughly symmetric, unimodal, and bell-shaped. Dodger Stadium. Photo credit losangeles.dodgers.mlb.com Sketch what this distribution should look like by drawing a bell-shaped curve and labeling the mean, mean ± 1 SD, mean ± 2 SD, and mean + 3 SD.
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
Transcribed Image Text:### 2014 Los Angeles Dodgers Season Analysis
In the 2014 MLB season, the Los Angeles Dodgers won 94 games and lost 68, clinching first place in the National League Western Division. During the regular season, which comprised 162 games, the Dodgers averaged 4.43 runs per game. The standard deviation of their runs per game stood at 2.88 runs. The distribution of their 162 run performances can be described as roughly symmetric, unimodal, and bell-shaped.
To visualize this distribution:
- **Mean (μ)**: 4.43 runs per game.
- **Standard Deviation (σ)**: 2.88 runs per game.
A bell-shaped curve, often referred to as a normal distribution, can be sketched to represent this data. On this curve:
- The peak of the bell, representing the mean (μ), should be labeled at 4.43.
- Moving one standard deviation to the left and right of the mean (μ ± 1σ), the values would be:
- Mean - 1 SD: 4.43 - 2.88 = 1.55
- Mean + 1 SD: 4.43 + 2.88 = 7.31
- Moving two standard deviations to the left and right of the mean (μ ± 2σ), the values would be:
- Mean - 2 SD: 4.43 - 2 * 2.88 = -1.33 (note: runs per game cannot be less than 0 in reality)
- Mean + 2 SD: 4.43 + 2 * 2.88 = 10.19
- Moving three standard deviations to the left and right of the mean (μ ± 3σ), the values would be:
- Mean - 3 SD: 4.43 - 3 * 2.88 = -4.21 (note: runs per game cannot be less than 0 in reality)
- Mean + 3 SD: 4.43 + 3 * 2.88 = 13.07
This curve can help in understanding the distribution and variability in the Dodgers' performance over the season.
#### Image Description
The image shows a vibrant scene of a baseball game at Dodger Stadium, with the stands filled with fans. The field is clearly visible with players in position, set against a backdrop of
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