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A product's demand in each period follows a normal distribution with mean of 60 and standard deviation of 10 . The lead time for this product is 3 periods. ( 36 points) a. The order-up-to level is 250 . What is the expected on-order inventory? (Give step by step details) (4 points) b. The order-up-to level is 250 . What is the expected on-hand inventory? (Give step by step details, including z score and how z is calculated) (12 points) c. The order-up-to level is 250 . What is the probability of stock-out? (Give step by step details) (4 points) d. To make sure there is only a 1.07% chance of running out of stock, what should be the order-up-to inventory level? (Give step by step details, including z score) ( 8 points)