Answer:
Approximately, 159 men weighs more than 165 pounds and 159 men weighs less than 135 pounds.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 150 pounds
Standard Deviation, σ = 15
We are given that the distribution of weights of 1000 men is a bell shaped distribution that is a normal distribution.
Formula:
![z_{score} = \displaystyle\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z_%7Bscore%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
P( men weighing more than 165 pounds)
P(x > 165)
Calculation the value from standard normal z table, we have,
![P(x > 165) = 1 - 0.8413 = 0.1587 = 15.87\%](https://tex.z-dn.net/?f=P%28x%20%3E%20165%29%20%3D%201%20-%200.8413%20%3D%200.1587%20%3D%2015.87%5C%25)
Approximately, 159 men weighs more than 165 pounds.
P(men weighing less than 135 pounds)
P(x < 135)
Calculation the value from standard normal z table, we have,
![P(x < 135) = 0.1587 = 15.87\%](https://tex.z-dn.net/?f=P%28x%20%3C%20135%29%20%3D%200.1587%20%3D%2015.87%5C%25)
Approximately, 159 men weighs less than 135 pounds.