Question 347795
A manufacture claims that 5% of the finished items coming off an assembly line each day are defective. A total of 5,000 items are produced a day, and 3 are randomly selected and inspected.
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a. If the manufacturer's claim is correct, what is the probability all 3 randomly selected items are defective?
(0.05)^3 = 0.000125 
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b. If all 3 randomly selected items are defective, would you infer the manufacturer's claim is incorrect? 
why?
No; the probability that would happen is extremely low.
The defect rate is probably higher.
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If the manufacturer's claim is correct, what is the probability none of the 3 items are defective?
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0.95^3 = 0.8574
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d. If none of the 3 items are defective, would you infer that the manufacturer's claim is incorrect? 
why?
His claim has not really been tested.  You would have no reason to
doubt it.
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Cheers,
Stan H.