The data give the market share (0 to 100%) of a brand-name pharmaceutical product in 224 metropolitan locations. The market share indicates the percentage of all prescriptions for this type of medication that are written for this brand.
(a) Describe the histogram and boxplot of the market shares. Is the histogram symmetric and unimodal? Would you say that this histogram is bell shaped?
(b) Are there any outliers? In what location does this brand have the highest market share? The lowest?
(c) The market share can only be as large as 100 and cannot be negative. Since a normal model allows for any value, is it possible for a normal model to describe these shares? Would a normal model be reasonable if the average share were closer to 0 or 100%?
(d) What normal model describes the distribution of returns of these shares?
(e) Is the normal model in part (d) a good description of these shares? Explain how you decided whether it’s a good match or not.