Problem 1. An opportunistic company is getting into the business of producing oatmeal bags with bits of Medina dates in

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Problem 1 An Opportunistic Company Is Getting Into The Business Of Producing Oatmeal Bags With Bits Of Medina Dates In 1 (81.82 KiB) Viewed 35 times

Problem 1. An opportunistic company is getting into the business of producing oatmeal bags with bits of Medina dates in them. It turns out that the number of pieces of dates in every bag of oatmeal produced is Poisson distributed, with mean 4.5. (a) Determine the variance of the number of date pieces in a bag. (b) What is the probability that a bag purchased by a random customer contains less than 2 pieces of dates? (In which case, the customer may feel cheated and attempt to file a complaint.) (c) Find the probability that a crate of 5 bags of oatmeal contains exactly 18 pieces of dates. (d) I have been purchasing and enjoying these oatmeal bags for many days in a row. What is the probability that a piece of date I find on the kitchen floor comes from a bag that contains exactly 5 pieces? (e) What is the expected number of pieces of dates that were in the same bag as the piece that I found on the kitchen floor? (f) In response to customer complaints, the company has implemented a robotic system with image recog- nition capability, that will inspect the production line and mark any bag that contains fewer than 2 pieces as unfit for the market. As a result of this process, compute the expected value and the variance of the number of date pieces in a randomly selected bag purchased at a store.