Week 4 Case Study According to the research done on the foot length of women, the mean length of women's feet is 9.58 inches with a standard deviation of 0.51 inch. Moreover, the distribution of foot length for women is bell shaped and, in fact, it has the appearance of the normal distribution. This distribution is useful to shoe manufactures, 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-toshoe-size conversion, obtained from Payless ShoeSource. http://www.payless.com/sizecharts/womens-footwear.html Submit the following questions in a single MS Word document. You must provide details of how you obtained your answer where requested. Use full, complete sentences when responding to the questions. Week 4 Case Study a) Based upon the mean foot length and standard deviation given above, use the technology tool of your choice to provide a sketch of the normal distribution curve for the length of women's feet. 5 points. b) What percentage of women have foot lengths between 9 and 10 inches? Be sure to include the z-scores for each. Provide details of your answer. 5 points. c) What percentage of women have foot lengths that exceed 11 inches? Provide details of your answer. 5 points. d) Shoe manufactures suggest that if a foot length is between two sizes, wear the larger size. Referring to the table of shoe size conversions, determine the percentage of women who wear size 8 shoes. Provide details of your answer. 5 points. e) If the owner of a chain store of shoe stores intends to purchase 10,000 pairs of women's shoes, roughly how many should he purchase of size 8? Explain your reasoning. 5 points