Problem 3. (15 points) Rivendaie Industries stocks a part that has a daily demand represented by the empirical distribution (shown in the table below). When restocking this part, the average lead time from the supplier is 3 days with a standard deviation of 0.5 days. The plant manager wants to determine how much safety stock to maintain for this part to ensure that stockouts will not be incurred in more than 5.5% of the order cycles

Daily demand (d) in units	Frequency
5	10
10	35
15	65
20	32
25	8

Total Observation = 150

Problem 3a (5 points) Find the mean and standard deviation for demand. (hint: see module 1 for discrete probability distributions)

Problem 3b. (5 points) Based on the information in problems 3 and 3a, what is the mean and standard deviation of demand during the lead time?

Problem 3c. (5 points) Based on the information in problems 3, 3a, and 3b, how much safety stock should the plant manager maintain to ensure that stockout will not be incurred in more than 5.5% of the order cycles? Express your answer as a whole number using standard rounding rules.

Problem 3d. (0 points) Upload a file. Use this question on the quiz to attach a file for this problem.