The number of imperfections in an object has a Poisson distribution with a mean λ =...

The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad quality." The numbers of imperfections in different objects are independent of each other. A random sample set of seven objects is taken. What is the probability that the sample set has exactly two top quality, two good quality, two normal quality, and one bad quality objects?

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If P(X) is an possion distribution then,

As solved in the above images, find the probability of object belonging to each type of quality Since the objects are taken randomly and imperfections in a object are independent the product of probability of each type of object yields the result

orchestra answered 1 year ago

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