It has been found that of the steel bars produced by a certain manufacturer, 0.5% are defective. (a) From a sample of 250 steel bars produced by the manufacturer, what is the probability that at least 3 are defective? [7 marks] (b) From a sample of 200 steel bars produced by the manufacturer, 3 were found to be defective. Can you infer that the manufacturing process is operating normally? [8 marks]

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