statistics

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this is the question which i have got from my teacher for homeworl and needed to show her on friday.

question 1. fred is in charge of inventory at the bedrock company. he would like to be able to guarantee a high service level, say at least 98%, for product p. this means that fred must find a policy which will ensure that there is always sufficient stock on hand to meet a variable demand pattern, as well as the uncertainty associated with delivery times.
freds current policy is to place an order for 30 units of product p whenever on-hand inventory falls to the reorder level of 15 units or less. having studied sales records for product p over the past six months, fred has now produced the following data tables for demand and lead times
daily demand for product p 0 1 2 3 4 5 6
probability 0.03 0.05 0.13 0.25 0.22 0.20 0.12
lead time (days) 1 2 3 probability 0.20 0.50 0.30 lost sales occur when there is insufficient stock on hand to meet demand. service level, expressed as a percentage, is defined as
service level = 1 - (lost sales)/(total demand) = (demand satisfied)/(total demand)
for example, if total demand is 60 and lost sales are 2, then service level = 12=60 = 96:7%.
assume that the beginning inventory is 30. simulate for 30 days in your simulation table.
(a)under the current policy and using 100 replicates, estimate the service level and the average inventory on hand. report 95% confidence intervals for both kpis.
(b)propose an inventory policy (reorder point and order quantity) that can reduce average inventory while satisfying the requirement of 98% service level. for this policy, report 95% confidence intervals for the service level and the average inventory on hand.
so this is the complete question
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