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I have a demand pattern for a service part. Demand event rate of this part is Poisson distributed. Demand of the part is 3 times in a year. So the demand event rate is 0.25/Month. Each demand transaction has different demand quantities. These demand quantities has certain distribution with mean of 100 and standard deviation of 120. Lead time of of the service part is 1 month. I want to identify what will be the demand quantity during its lead time of 1 month for probability of 95%. I want to use compound Poisson to address this problem

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