Pizza U.S.A., Inc., produces and markets pizzas on a national basis. The shop manager decides how many pizzas to be made. He learns that daily demand for pizza follows a normal distribution of mean 150 and standard deviation 30.

Part a:

The manager estimates that he will be able to make a profit if he sells more than 200 pizzas. The manager expects to get an incentive only if he makes a profit. What is the probability that the manager will receive an incentive?

Part b:

The manager is also aware that if the sale drops below 100, then he receives a pay-cut. What is the probability that he will receive a pay cut?

Part c:

What is the probability that pizza sales are within 20% of the average value (mean demand)?

Part d:

If the manager has materials to make only 168 pizzas for a given day with the raw materials available with him, how much are the expected lost sales assuming there is no way that additional raw materials can be purchased for that day?

Part:

If the manager wants the expected lost sales to be 15 pizzas or lower, then how much raw materials (equivalent to how many pizzas) must he store at the beginning of the day?