In a quality control scheme at a factory, batches of components are accepted or rejected depending on

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In a quality control scheme at a factory, batches of components are accepted or rejected depending on the number of defective items counted in a sample. Rejected batches are inspected and all defective items are replaced with good ones. From the machine reliability statistics it has been calculated that the probabilities of three, four, five, six and seven defective items in a rejected batch are 0.3, 0.4, 0.2, 0.08 and 0.02 respectively. Fifty rejected batches produced a total of 221 defective items. Does this suggest that the machines are producing more defective items than they should?

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