Answer:
The number of men weighing more than 165 pounds is about 84.13%, and the number of men weighing less than 135 pounds is about 15.87%.
Explanation:
To find the number of men weighing more than 165 pounds and the number of men weighing less than 135 pounds in a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds, we can use z-scores and the standard normal distribution table (z-table).
1. For the number of men weighing more than 165 pounds:
First, we need to calculate the z-score for 165 pounds:
\(Z = \frac{X - \mu}{\sigma} = \frac{165 - 150}{15} = 1\)
Now, we can find the probability that a randomly selected man weighs more than 165 pounds using the z-table. A z-score of 1 corresponds to a probability of approximately 0.8413. So, about 84.13% of men weigh more than 165 pounds.
2. For the number of men weighing less than 135 pounds:
Similarly, we calculate the z-score for 135 pounds:
\(Z = \frac{X - \mu}{\sigma} = \frac{135 - 150}{15} = -1\)
Using the z-table, a z-score of -1 corresponds to a probability of approximately 0.1587. So, about 15.87% of men weigh less than 135 pounds.
Therefore, the number of men weighing more than 165 pounds is about 84.13%, and the number of men weighing less than 135 pounds is about 15.87%.