Matt's uses a fixed order interval inventory system. Demand per month is 80 units with a standard deviation of 50units per month. Lead time has been shown to be 2 months. John's believes reviewing the inventory level every 4 months is the ideal policy, and that a service level of 85% is acceptable.

If the current inventory position is 450 units, and it is time to place an order, what order quantity should be placed?

What is the probability that John's will run out of inventory before the next order arrives?