Paul has been working for a shop selling smart phones. He was recently promoted to the shop manager. Being a new manager, Paul decided to introduce a new inventory control system to his shop to reduce operating cost. Answer to the questions below.

4.1Assume that the number of shoppers visiting his store follows Poisson distribution with a mean of 12 a day. Out of these shoppers, 25% make actual purchase whereas remaining 75% do not. How many cell phones should he at least keep every day so that probability of not being able to meet daily demand does not exceed .05?

4.2Assume that the number of shoppers visiting his store follows Binomial distribution with n = 20 and p = .20. How many cell phones should he at least keep every day so that probability of not being able to meet daily demand does not exceed .05?