Inventory. A merchant knows that the number of a certain kind of item that he can sell in a given period of time is Poisson distributed. How many of these items should the merchant stock, so that the probability will be 0.95 that he will have enough items to meet the customer demand for a time period of length T? Let v denotes the mean rate of occurrence per unit time and K the unknown quantity he should stock. Solve now the following point.

a. If the merchant sells an average of two items per day, how many should he stock so that he will have a probability at least 0.95 of having enough stock to meet the demand in 1-month period? (Hint: we denote X as the demand and K as the stock of the items and the solution requires finding K so that P½X  K  0:95 or P K k ¼ 0 eð2,30Þ ð60Þ k k!  0:95.)