Question

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

Answer 1

68% fall within +/- 1 SD, so men above that 1 SD (165) are: (100-68)/2
32/2 = 16% above 165 and also 16% below 135

Answer 2

Explanation:

Let X be the weights of 1000 men in a certain town.

Given that X is N(150, 15)

P(X>165) = P(Z>1) =0.5-0.3413 = 0.1687

No of men weighing more than 165 pounds in 1000 men = 1000(0.1687)

=168.7 =169 men apprxy.

Similarly

P(X<135) = P(Z<2)=0.5-0.4775 = 0.0225

No of men weighing less than 135 pounds is about =0.0225(1000)

= 22.5

=22