25 Sep Buford has generously offered to assist the Fireside Girls troop 46231

Buford has generously offered to assist the Fireside Girls troop 46231 in their annual cheese sale. Last year, there was a significant amount of cheese left over due to patrons not picking up (and paying for) their orders. Buford feels that it’s hard not to place an order when the Fireside girls come knocking on your door, but then there is less motivation to actually follow through with the purchase absent the sales pressure. Requiring a deposit at the time of order may help with this issue. The town of Danville has about 3000 potentially interested customers. The probability that a customer will place an order will decline as the required deposit increases, however, as the deposit amount increases, there is a higher probability that a customer who placed an order will actually pick up the cheese and pay the balance. The table in the spreadsheet shows that relationship. Note that these probabilities apply independently to all customers, and are not a blanket percentage of all customers. You will need to create a random variable for customers placing and order and a random variable for customers picking up an order.

It is also not certain how much cheese will actually be available. Buford’s nerdy friend has run some calculations and believes that the amount of cheese that they can acquire for sale will be normally distributed with a mean of 1600 orders and a standard deviation of 150 orders. If there is insufficient cheese to fill an order when a customer arrives at pickup, then the amount of the deposit must be refunded on the spot. If a customer placed a pre-order but doesn’t show up to pickup the cheese, then they don’t know you ran out and there is no reason to refund their deposit. Round the number of orders available down to the nearest whole number since no one wants part of an order.