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)