Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in (based on anthropometric survey data from Gordon, Churchill, et al.). If one male is randomly selected, find the probability that his head breadth is less than 6.2 in. Find the probability that 30 randomly selected men have a mean head breadth less than 6.2 in. State why the central limit theorem can be used.
Find the probability that 100 randomly selected men have a mean head breadth less than 6.2 in. State why the central limit theorem can be used.