A TV manufacture is supplied with a certain component by a specialist producer. Each incoming consignments...

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A TV manufacture is supplied with a certain component by aspecialist producer. Each incoming consignments is subject to thefollowing quality control procedure. A random sample of 10components is individually tested. If there are one or moredefective components among the 10 tested, the entire consignment isrejected. If there are no defective components in the sample, theconsignment is accepted.
i)What are the probabilities of a consignment being rejected ifthe true proportions of defective components are:
1) 1%
2) 10%
3) 30%
ii) if a sample of 20 components ( instead of 10) weretested,and the consignment rejected if two or more proveddefective, calaculate the probabilities of rejecting a consignmentfor the same proportions of defective components( i.e 1%,10% and30%)
iii) which quality control procedure do u think is thebetter

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According to the given question a random sample of 10components is individually tested If there are one or more defectivecomponents among the 10 tested the entireconsignment is rejected If there are no defective components inthe sample the consignment is acceptedLet us define be the event that thenumber of defective components in the sampleTherefore follows binomialdistribution with the probability mass function ofwith pmf aswhere is the true proportionsof defective components i The probabilities of a consignment being rejected if the See Answer

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