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Answer :
Final answer:
Using the empirical rule, we find that approximately 99.7% of the men's heights fall within the range of 162 cm and 204 cm (which is three standard deviations around the mean), and approximately 68% of the men's heights fall within the range of 176 cm and 190 cm (which is one standard deviation around the mean).
Explanation:
The subject question can be answered using the empirical rule, which states that approximately 68%, 95%, and 99.7% of observation values fall within one, two, and three standard deviations around the mean, respectively. This works specifically when the values of a dataset follow a bell-shaped or normal distribution. As the heights of men on this baseball team are normally distributed, you can translate these rules into the actual measurements by adding and subtracting multiples of the standard deviation from the mean.
a. For the range of 162 cm - 204 cm:
Subtracting and adding three times the standard deviation from the mean (183 cm ± 3*7 cm), we get the interval from 162 cm to 204 cm. According to the empirical rule, about 99.7% of the men's heights should fall within this range.
b. For the range of 176 cm - 190 cm:
The interval from 176 cm to 190 cm is equivalent to subtracting and adding one standard deviation from the mean (183 cm ± 7 cm), which according to the empirical rule, corresponds to about 68% of the men's heights.
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