# statistics question

In human engineering and product design, it is important to consider people’s weights so that airplanes or elevators aren’t overloaded. Based on data from the National Health Survey, the weight for adult males in the United States follows a normal distribution with a mean weight of 173 pounds and a standard deviation of 30 pounds.

a. If one U.S. adult male is randomly selected from the U.S. population, what is the probability that his weight will be greater than 200 pounds? (6 points)

b. If a sample of 36 U.S. adult males are randomly selected, what is the probability that the sample mean weight will be greater than 200 pounds? (6 points)

c. Assume I work for an airline based in the Quad Cities. I need to provide my supervisor with an estimate of the mean male weight on each flight. There are too many male passengers (about 100 men) on each flight so I don’t have time to interview all of them. My supervisor tells me that I can choose one of the following 2 options to estimate the average male weight on each flight:

Option 1: Collect data on 10 samples of 5 men each.
Option 2: Collect data on 25 men (just one sample).

Which option do you choose and why? (6 points)