The warehouse manager of a department store manages his products based on the classic EOQ model of inventory management, even though he knows that the demand for his products is uncertain. At this time and before transferring the management of its inventories to a probabilistic model, it has decided to continue with the parameters and variables of the EOQ model for its type C products but integrating a safety inventory that comply with a 95% service level ( 5% risk probability) in these products. Determine the safety inventory level for a product with a reorder point of 450 units (based on the EOQ model) and facing uncertain demand during its lead time based on:

a) a normal probability distribution with mean 450 units and standard deviation of 50 units.

b) a uniform probability distribution with a minimum value of 300 units and a maximum of 600 units.

c) a discrete probability according to the following historical values:

Demand, D 300 350 400 450 500 550 600

Probability, f(D) 0.10 0.15 0.15 0.20 0.15 0.15 0.10