Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 15.2 cm and a standard deviation of 2.5 cm (based on anthropometric survey data from Gordon, Churchill, et al.).
a. What percentage of men have head breadths greater than 17 cm? If helmets are made to accommodate only males with head breadths less than 17 cm, would those helmets exclude too many males?
b. If, due to financial constraints, the helmets are designed to fit all men except those with head breadths that are in the smallest 5% or largest 5%, find the minimum and maximum head breadths that the helmets will fit.