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The heights of men have a bell-shaped distribution with a mean of 176 cm and a standard deviation of 7 cm. Use the empirical rule to find the percentage of men who are less than 183 cm.

1. 84%
2. 5%
3. 16%
4. 95%
5. 68%

Answer :

Final answer:

According to the empirical rule for normal distributions, approximately 84% of men should have a height less than 183cm since this value lies within 1 standard deviation of the mean

Explanation:

The problem involves understanding normal distributions and the empirical rule. The empirical rule states that for any bell shaped or normal distribution, roughly 68% of the observed values fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In this case, the mean height is 176cm, with a standard deviation of 7cm.

To find the percentage of men who are less than 183cm tall, we calculate the number of standard deviations 183cm is from the mean. This gives us 1 standard deviation. Therefore, using the empirical rule, the percentage of men less than 183cm tall is 50% (from the left half of the bell curve) added to 34% (which represents the first half of the second standard deviation), for a total of 84%.

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