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Answer :
The empirical rule tells you ...
a) 68% are within 1 standard deviation of the mean
b) 95% are within 2 standard deviations of the mean
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Final answer:
To find the approximate percentage of men between the given values, use the empirical rule with z-scores. For a), approximately 68% of men are between 167 cm and 185 cm. For b), approximately 95% of men are between 158 cm and 194 cm.
Explanation:
To find the approximate percentage of men between the given values using the empirical rule, we first need to convert the values to z-scores. The z-score formula is: z = (x - mean) / standard deviation. For a), the z-scores are -1 and 1. For b), the z-scores are -2 and 2. Using the empirical rule, we know that approximately 68% of values lie within 1 standard deviation of the mean, 95% lie within 2 standard deviations, and 99.7% lie within 3 standard deviations. Therefore, approximately 68% of the men are between 167 cm and 185 cm, and approximately 95% are between 158 cm and 194 cm.
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