High School

The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.

From the data, we can conclude that:

1. The number of men weighing more than 165 pounds is ______.
2. The number of men weighing less than 135 pounds is ______.

Answer :

Final answer:

About 16% or 160 out of 1000 men in the town weigh more than 165 pounds, and similarly, the same number of men weigh less than 135 pounds.

Explanation:

A standard deviation of 15 pounds means that scores within one standard deviation of the mean (i.e., numbers between 135 and 165 pounds) represent about 68% of the scores. Hence, weights either less than 135 pounds or more than 165 pounds represent about 32%.

Assuming that the split between those weighing less than 135 pounds and those weighing more than 165 pounds is equal, i.e., 16% each. So, 16% of 1,000 men is 160. Therefore, the number of men weighing more than 165 pounds is approximately 160, and the number of men weighing less than 135 pounds is also approximately 160.

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