Marine Corps Height Requirements for Men The U.S. Marine Corps requires that men have heights between 64 in. and 78 in. (The National Health Survey shows that heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in.)

a. Find the percentage of men meeting those height requirements. Are too many men denied the opportunity to join the Marines because they are too short or too tall?

b. If you are appointed to be the Secretary of Defense and you want to change the requirement so that only the shortest 2% and tallest 2% of all men are rejected, what are the new minimum and maximum height requirements?

c. If 64 men are randomly selected, find the probability that their mean height is greater than 68.0 in.