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Answer :
According to the 68-95-99.7 rule for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In a normal distribution, the mean (μ) represents the center of the distribution, and the standard deviation (σ) determines the spread or dispersion of the data around the mean. For this problem, the mean (μ) is 74 strokes and the standard deviation (σ) is 3 strokes. To visualize this, we can sketch a bell-shaped curve representing the normal distribution, centered at 74 strokes.
Next, using the 68-95-99.7 rule:
1. Approximately 68% of the data falls within one standard deviation of the mean, which means golfers who score between 71 and 77 strokes account for 68% of the distribution.
2. About 95% of the data falls within two standard deviations of the mean, so golfers who score between 68 and 80 strokes make up 95% of the distribution.
3. Approximately 99.7% of the data falls within three standard deviations of the mean, indicating that golfers who score between 65 and 83 strokes represent 99.7% of the distribution.
By understanding these percentages, golf course managers can gain insights into the performance of players and set realistic expectations. Additionally, this information can be useful for evaluating golfers' progress over time and identifying areas for improvement.
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