Answer :
Final answer:
The correct summary of the data is that about 160 people weigh more than 165 pounds, based on the empirical rule for a normal distribution.
Explanation:
To summarize the data of the measured weights of 1,000 men in a certain village, which follows a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds, we can use the empirical rule (68-95-99.7). According to this rule, approximately 68% of data values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
In this context, since 165 pounds is one standard deviation above the mean (150 + 15 = 165), it means approximately 16% of men (100% - 84%) will weigh more than 165 pounds, which translates to about 160 people (0.16 * 1000).
Therefore, the correct summarization is: About 160 people weigh more than 165 pounds.
