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# Introduction to Statistics and Econometrics Essay

1. Specialty faces the decision of how many Weather Teddy units to order for the coming holiday season. Members of the management team suggested order quantities of 15000, 18000, 24000 or 28000 units. The wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team asks you for an analysis of the stock-out probabilities for various order quantities,

an estimate of the profit potential, and to help make an order quantity recommendation. Specialty expects to sell Weather Teddy for \$24 based on a cost of \$16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventory for \$5 per unit After reviewing the sales history of similar products, Specialty’s senior sales forecaster predicted an expected demand of 20,000 units with a 0.95 probability that demand would be between 10,000 units and 30,000 units. Questions

1. Approximate the demand distribution using Normal distribution and sketch the distribution. 2. Compute the probability of a stock-out for the order quantities suggested by members of the management team. 3. Compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales is 10,000 units, most likely case in which sales is 20,000 units and best case in which sales is 30,000 units

Questions
1. One of Specialty’s managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What quantity would be ordered under this policy, and what is the projected profit under the three
sales scenarios? 2. Provide your own recommendation for an order quantity and note the associated profit projections.

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