For the coming season, Specialty Toys, Inc plans to introduce the new product called Weather Teddy. Specialty managers claimed Weather Teddy gave predictions that were as good as many local TV weather forecasters!
Now, Specialty encounters the decision of how many Weather Teddy units to order from manufacturer for the coming holiday season. Members of the management team suggested four order quantitites of 15,000, 18,000, 24,000, or 28,000 units. The team asks you for the analysis of the stock-out probabilities for different order quantities, an determine of the profit potential, and to help make an order recommendation.
Specialty expects to sell Weather Teddy for $24 based upon the unit cost of $16. If inventory remains after the holiday season, Specialty will sell all surplus inventory for $5 per unit. After reviewing sales history of similar products, Specialty's senior sales forecaster predicted that the demand would be basically distributed with the mean as 20,000 units and that demand would be between 10,000 and 30,000 units with a 90% probability.
Calculate the probability of quantity demanded less than 5,000 units.