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A consumable commodity on an assembly line is used at a constant rate that can be modeled according to a Poisson process

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A consumable commodity on an assembly line is used at a constant rate that can be modeled according to a Poisson process. (Poisson Process). 

a. Explain the assumptions behind modeling a process as a Poisson process.

 b. If the inventory is 20 pieces, and they are consumed at a mean rate of 2 per hour calculate the probability that all will be gone in 6 hours.

 c. Plot the probability distribution for the time it takes for all of the parts to be consumed between 1 and 25 hours.