The fast-food restaurant Five-Guys operates on national basis. The store manager of Five Guys on Iowa Street has to decide how many "Cheese Dogs" to make every day. He learns that daily demand for Cheese Dogs follows a normal distribution of mean 100 and standard deviation 16.

(e) If the manager has materials to make only 128 Cheese Dogs for a given day with the raw materials available with him, how much is the expected inventory at the end of the day assuming there is no way that additional raw materials can be purchased on that day? [4 points]

(f) If the manager wants the expected inventory at the end of the day to be 15 dogs or lower, then how much raw materials (equivalent to how many Cheese Dogs) must he store at the beginning of the day? [4 points]