Specialty Toys, Inc., sells a variety of new and innovative children's toys. As with other products, Specialty faces the decision of how may Weather Teddy units to order for coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential. The product management team ask you for analysis of the stock-out probabilities for various order quantities, an estimate of the product potential, and to help make an order quantity recommendation. Specialty expects to sell Weather Teddy for $24 based on 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%u2019s sales forecaster predicted and expected demand of 20,000 units with a .95 probability that demand would be between 10,000 units and 30,000 units.

Prepare a managerial Report that addresses the following issues and recommends an order quantity for the Weather Teddy product.

1. Use the sales forecaster%u2019s, predictions to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its means and standard deviation.

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 equal 10,000 units, most likely case in which sales equal 20,000 units, and best case in which sales equal 30,000 units.

4. One of Specialty%u2019s manager 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 order under this policy, and what is the projected profit under the three sales scenarios?

5. Provide your own recommendations for an order quantity and note the associated profit projections. Provide a rationale for you recommendation