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------------------------------------------------ Heights of men on a baseball team have a bell-shaped distribution with a mean of 180 cm and a standard deviation of 6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?

a. 168 cm and 192 cm

b. 174 cm and 186 cm

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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