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A distributor receives a very large shipment. The distributor would like to accept the shipment if 15% or fewer of the items are defective and to return it if more than 15% of the components are defective. Someone on the quality assurance team samples 4 items. Let X be the random variable for the number of defective items in the sample. You can assume that the defectiveness of items is independent within the shipment. Also assume that exactly 15% of the items in the shipment are defective. Determine the probability distribution of X (write out the pmf) using probability theory. x P(X=x)
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