For the coming season, Specialty Toys, Inc plans to introduce a new product called Weather Teddy. Specialty 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 the 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 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 $16. 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 that the demand would be normally distributed with the mean as 20,000 units and that demand would be between 10,000 and 30,000 units with a 90% probability.
Using the sales forecaster prediction to calculate, what is the standard deviation for the demand distribution?