In operations management, you learn that intermittent systems produce a variety

Question

In operations management, you learn that intermittent systems produce a variety of products one at a time (or in batches) to customer order. These systems contrast with continuous systems, in which a large number of homogeneous products are produced. One feature of intermittent systems is that new orders arrive at irregular intervals. For example, orders for business letterhead may come into the Ben Franklin Print Shop at the rate of .5 per day. Find the probability of (a) at least 2 orders for letterhead arriving tomorrow, (b) no orders in the next 2 days. (c) Find the expected number of orders in the next 30 working days. (d) What is the probability that the time between two orders is less than one day?

Explanation / Answer

Given X~Poisson(=0.5)

P(X=x)=(0.5^x)*exp(-0.5)/x!

(a) at least 2 orders for letterhead arriving
tomorrow

P(X>=2)=1-P(X=0)-P(X=1)=0.09020401

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