Answer to Question #218375 in Statistics and Probability for Areeb

Question #218375

Large Consignments of computer components are inspected for defectives by means of a sampling system. Ten components are examined and the lot is to be rejected if two or more are found to be defective. If a consignments contains exactly 10% defectives. Find the probability of the consignment by using the technique of Binomial probability distribution that the consignment is: i) Accepted ii) Rejected


1
Expert's answer
2021-07-19T05:45:25-0400

Let X=X= the number of defective components: XBin(n,p).X\sim Bin(n, p).

Given n=10,p=0.1,q=1p=10.1=0.9.n=10, p=0.1, q=1-p=1-0.1=0.9.

i)


P(X<2)=P(X=0)+P(X=1)P(X<2)=P(X=0)+P(X=1)

=(100)(0.1)0(0.9)100+(101)(0.1)1(0.9)101=\dbinom{10}{0}(0.1)^0(0.9)^{10-0}+\dbinom{10}{1}(0.1)^1(0.9)^{10-1}

=0.7360989291=0.7360989291

The probability that the consignment is accepted is 0.7360989291.



ii)


P(X2)=1P(X<2)P(X\geq2)=1-P(X<2)

=1(100)(0.1)0(0.9)100(101)(0.1)1(0.9)101=1-\dbinom{10}{0}(0.1)^0(0.9)^{10-0}-\dbinom{10}{1}(0.1)^1(0.9)^{10-1}

=0.2639010709=0.2639010709


The probability that the consignment is rejected is 0.2639010709.



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