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Anything that is mathmatical the work has to be shown, I will need this by 2pm est.

6. Scorekeeper, Inc., manufactures stadium scoreboards. Table 1 illustrates the demand for Scorekeeper’s scoreboards over the past 25 days. The mean of daily demand is 6 units.

PS-5-438

Table 1

Day	Demand	Day	Demand
1	4	14	6
2	3	15	4
3	4	16	2
4	6	17	5
5	7	18	6
6	8	19	7
7	6	20	6
8	5	21	6
9	6	22	5
10	10	23	7
11	8	24	8
12	7	25	9
13	5

a. Is the demand distribution normal? How do you know?

b. Calculate the standard deviation for daily demand. Assume in this case that the performance cycle is constant.

Table 2 summarizes Scorekeeper’s performance cycles over the past 40 replenishments. The expected cycle duration is 12 days.

Table 2

Performance Cycle	Frequency
(in days)	(f)
10	4
11	8
12	16
13	8
14	4

c. Is the performance cycle distribution normal? How do you know?

d. Calculate the standard deviation for the performance cycle.

e. Given your answers to parts (b) and (d), find the safety stock required at 1 combined standard deviation under conditions of demand and performance cycle uncertainties.

f. If the typical order quantity is 36 units, find the average inventory at 3 standard deviations under demand and performance cycle uncertainty.

g. Scorekeeper is striving for a 99 percent product availability level. Given the above information as well as your answer to (e), find the function value of the normal loss curve, f(k).

h. Use Table 6-14 to find the value for k, given your answer to part (g), and calculate the required safety stock for the desired 99 percent availability level.

i. What would be the required safety stock for 99 percent availability should the order quantity change to 30 units?