Chapter 6, Problem 6.1.1CP

Specialty Toys
Specialty Toys, Inc. sells a variety of new and innovative children's toys. Management learned that the preholiday season is the best time to introduce a new toy, because many families use this time to look for new ideas for holiday gifts. When Specialty a new toy with good market potential, it chooses an October market entry date.
In order to get toys into its stores by October, Specialty places one-time orders with its manufactures in June or July of each year. Demand for children's toys be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits be realized. However, toys can also flop, leaving Specialty stuck with high levels of inventory that must sold at reduced prices. The most important question the faces is deciding how many units of a toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in sales.
For the coming season, plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child presses Teddy's hand, the bear begins to talk. A built-in barometer selects of five responses that predict the weather conditions. The responses range from "It looks to be a very nice day! Have to "I think it may rain today. Don't forget your umbrella." Tests with the product show that, even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of Specialty's managers claimed Teddy gave predictions of the weather that were as good as those of many local television weather forecasters.
As with other products, 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 15,000, 18,000, or 28,000 units. The wide range of order quantities suggested indicates 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 help with making 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 .95 probability that demand would be between 10,000 units and 30,000 units

Managerial Report
Prepare a managerial report that addresses the following issues and recommends an order quantity for the Weather Teddy product.
1. Use the sales forecaster' s prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.