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 the number of men weighing more than 165 pounds is about , and the number of men weighing less than 135 pounds is about .

Okay let's write everything we know:

n = 1000
σ = 15
μ = 150
 
Now let's draw the normal distribution (look at picture all the way on the bottom of this post)

We can observe that 165 and 135 are both 15 away from 150. That means that 165 and 135 are one standard deviation from the mean. You should be familiar with 68–95–99.7% rule. It tells us that the probability of someone being between one standard deviation or in our case between 135<x<165 pounds is 68%.
For two standard deviation is 95%, and for three is 99.7%.

Now we know that 68% of people are between 135<x<165. That means that 32% of a 1000 men are either more than 165 pounds or less than 135 pounds.

So 320 men weigh more than 165 or less than 135.
We divide that (we can because normal distribution is even) and get
About 160 men that weigh more than 165
About 160 men that weigh less than 135

More accurate would be 158.66 men for both, because we used 68% instead of more correct 68.27%

There's a site where you can test your answers on an online calculator:

 http://homepage.stat.uiowa.edu/~mbognar/applets/normal.html