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Some companies such as Demand Tec have developed software to

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, and 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.

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, and 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.

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