Answer to Question #217926 in Statistics and Probability for Ariz

Question #217926
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
2021-07-19T07:37:26-0400

n=10

p=0.1

q=0.9

X~Binomial(10,0.1)

"P(X) = C^{10}_x(0.1)^x(0.9)^{10-x}"

i) Accepted if

"P(X<2) = P(X=0)+P(X=1) \\\\\n\nP(X=0) = \\frac{10!}{0!(10-0)!} \\times (0.1)^0 \\times (0.9)^{10-0} \\\\\n\n= 1 \\times 1 \\times 0.3486 \\\\\n\n= 0.3486 \\\\\n\nP(X=1) = \\frac{10!}{1!(10-1)!} \\times (0.1)^1 \\times (0.9)^{10-1} \\\\\n\n= 10 \\times 0.1 \\times 0.3874 \\\\\n\n= 0.3874 \\\\\n\nP(X<2) = 0.3486 + 0.3874 = 0.736"

ii) Rejected if

"P(X\u22652) = 1 -P(X<2) \\\\\n\n= 1 -0.736 \\\\\n\n= 0.264"


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