Answer :
The approximate percentage of men with heights between 155 cm and 197 cm is 100 %.
The empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline used to estimate the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.
To use the empirical rule, we need to determine the number of standard deviations that correspond to the given heights. First, we calculate the z-scores for the lower and upper bounds of the height range:
Lower bound: z = (155 - 176) / 7 = -3
Upper bound: z = (197 - 176) / 7 = 3
Now, we can apply the empirical rule. According to the rule:
- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.
Since the range between -3 and 3 standard deviations covers the entire distribution, we can conclude that approximately 100% of the data falls within this range.
Therefore, the approximate percentage of men with heights between 155 cm and 197 cm is 100%.
To know more about standard deviations refer here:
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