For the coming season, Specialty Toys, Inc., plans to introduce a new product ca

Question

For the coming season, Specialty Toys, Inc., plans to introduce a new product called Weather Teddy. Specialty’s managers claimed Weather Teddy gave predictions that were as good as many local TV weather forecasters! Now, Specialty faces the decision of how many Weather Teddy units to order from manufacturers for the coming holiday season. Members of the management team suggested four order quantities of 15,000, 18,000, 24,000, or 28,000 units. The 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 recommendation. Specialty expects to sell Weather teddy for $24 based on the unit cost of $20. If inventory remains after 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 that the demand would be normally distributed with the mean as 20,000 units and that demand would be between 5,000 and 35,000 units with a 90% probability.

2. Compute the probability of quantity demanded less than 7,500 units.

Explanation / Answer

mean = 20000

For 90% CI, z-value = 1.65

5000 = 20000 - 1.65*SE
SE = 15000/1.65 = 9090.9091

Different stock out probabilities are

2.

P(X < 7500) = P(z < (7500 - 20000)/9090.9091) = P(z < -1.375) = 0.0846

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