Women’s Shoes. Research reveals that foot length of women is normally distributed with mean 9.58 inches and standard deviation 0.51 inch. This distribution is useful to shoe manufacturers, shoe stores, and related merchants because it permits them to make informed decisions about shoe production, inventory, and so forth.

Along these lines, the following table provides a foot-length-to-shoesize conversion, obtained from Payless ShoeSource.

Length (in.) Size (U.S.) Length (in.) Size (U.S.)

8 3 10 9 8 3 16 3 1 2 10 3 16 9 1 2

8 5 16 4 10 5 16 10 8 8 16 4 1 2 10 8 16 10 1 2

8 11 16 5 10 11 16 11 8 13 16 5 1 2 10 13 16 11 1 2

9 6 11 12 9 3 16 6 1 2 11 3 16 12 1 2

9 5 16 7 11 5 16 13 9 8 16 7 1 2 11 8 16 13 1 2

9 11 16 8 11 11 16 14 9 13 16 8 1 2

a. Sketch the distribution of women’s foot length.

b. What percentage of women have foot lengths between 9 and 10 inches?

c. What percentage of women have foot lengths that exceed 11 inches?

d. Shoe manufacturers suggest that if a foot length is between two sizes, wear the larger size. Referring to the preceding table, determine the percentage of women who wear size 8 shoes; size 111

/2 shoes.

e. If an owner of a chain of shoe stores intends to purchase 10,000 pairs of women’s shoes, roughly how many should he purchase of size 8? of size 111

/2? Explain your reasoning.