Some companies, such as Demand Tec, have developed software to help retail chains set prices that optimize their profits. An Associated Press story (April 28, 2007) about this software described a case in which a retail chain sold three similar power drills: one for $90, a better one for $120, and a top-tier one for $130. Software predicted that by selling the middle-priced drill for only $110, the cheaper drill would seem less a bargain and more people would buy the middle-price drill.
a. For the original pricing, suppose 50% of sales were for the $90 drill, 20% for the $120 drill, and 30% for the $130 drill. Construct the probability distribution of X = selling price for the sale of a drill, find its mean, and interpret,
b. For the new pricing, suppose 30% of sales were for the $90 drill, 40% for the $110 drill, and 30% for the $130 drill. Is the mean of the probability distribution of selling price higher with this new pricing strategy? Explain.