Engineers must consider the breadths of male heads when designing motorcycle helmets for men. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of l .0 inch (based on anthropometric survey data from Gordon, Churchill et al.).
a. If one male is randomly selected, what is the likelihood that his head breadth is less than 6.2 inches?
b. The Safeguard Helmet company plans an initial production run of 100 helmets. How likely is it that 100 randomly selected men have a mean head breadth of less than 6.2 inches?
c. The production manager sees the result in part b and reasons that all helmets should be made for men with head breadths of less than 6.2 inches, because they would fit all but a few men. What is wrong with that reasoning?