In designing gloves for women, it is found that the lengths of their hands are normally distributed with a mean of 175mm and a standard deviation of 9 mm (based on anthropometric survey data from Gordon, Churchill, et al.).
a. What percentage of women have hands longer than 185 mm? If no gloves are made to fit hands longer than 185 mm, would a large percentage of the market be lost?
b. Find the 5th percentile and 95th percentile for the lengths of women’s hands.