Answer :
Final answer:
Applying the empirical rule to the given scenario, approximately 95% of the baseball team's heights is expected to be between 168 cm and 192 cm, and approximately 68% is expected to be between 174 cm and 186 cm.
Explanation:
The empirical rule, which is also known as the 68-95-99.7 rule, is used in statistics to estimate where the values lie within a statistical data set. In a normal distribution:
- Approximately 68% of the data falls within 1 standard deviation of the mean
- Approximately 95% within two standard deviations
- Approximately 99.7% within three standard deviations
In your case, the mean height is 180 cm and the standard deviation is 6 cm. Therefore:
- For the heights between 168 cm (mean - 2 standard deviations) and 192 cm (mean + 2 standard deviations), the approximate percentage is 95% according to the empirical rule.
- For the heights between 174 cm (mean - 1 standard deviation) and 186 cm (mean + 1 standard deviation), the approximate percentage is 68% according to the empirical rule.
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