Poke 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 December holiday gifts.When Poke discovers a new toy with good market potential, it chooses an October market entry date.

In order to get toys in its store by October, Poke places one time orders with its manufacturers in June or July of each year.Demand for children's toys can 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 can be realized.However, new toys can also flop, leaving Poke stuck with high levels of inventory that must be sold at reduced prices.The most important question the company faces is deciding how many units of a new 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 clearance sales.

For the coming season, Poke plans to introduce a new product called Chatty Bear.This variation of a talking Bear teddy bear is made by a company in Korea.When a child presses Bear's hand, the bear begins to talk.A built-in barometer selects one of the five responses that predicts the weather conditions.The responses range from "it looks to be a very nice day! Have fun" 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 Poke's managers claimed Bear gave predictions of the weather that were as good as many local television weather forecasters.

As with other products, Poke faces the decision of how many Chatty Bear units to order for the coming holiday season.Members of the management team suggested order quantities of 15,000, 18,000, 24000, or 28000 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 to help make an order quantity recommendation.Poke expects to sell Chatty Bear for $24 based on a cost of $16 per unit.If inventory remains after the holiday season, Poke will sell all surplus inventory for $5 per unit.After reviewing the sales history of similar products, Poke senior sales forecaster predicted an expected demand of 20,000 units with a 0.9 probability that demand would be between 10,000 and 30,000 units.

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.
2. Compute the probability of a stock-out for the order quantity 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 = 10,000 units, most likely case in which sales = 20,000 units and the best case in which sales = 30,000 units.
4. One of Poke's managers felt that the profit potential was so great that order quantity should have a 70% chance of meeting demand and only 30% chance of any stock outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?
5. Provide your own recommendation for an order quantity and note the associated profit projections. Provide a rational for your recommendation.

I don't know how to do problem 4. Can you help me with this?