In February, the owner of a Fan Supplies, Inc., must place an order with Nike for the new shirts for the coming season. The long lead time is required for the contract manufacturers in Asia to order the necessary materials and to begin production in April. The shirts will be delivered in early-August just in time for the new season. Nike will charge $50 for each shirt ordered, and he will sell each shirt for $75 during the season. There will not be another opportunity to order any more shirts if he runs out. At the end of the season, they will sell all the shirts that are left at a price of $15. Obviously, he doesn’t know exactly what the demand for these shirts will be, but during the past couple of years he has sold an average of 500 shirts each season. Based on historical sales the demand for shirts appears to be normally distributed with a standard deviation of 75. He is planning to order 550 shirts this year.
1) Estimate of the distribution of total profit for this order.
2) Estimate mean total profit for this order.
3) Estimate the probability that he will incur a net loss on this order.