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Answer on Statistics and Probability Question for Hasmukh

Question #8911
In the screws manufactured by a certain machine, 3 percent are found to be defective. If a
sample of 12 is taken, what is the probability that (5 Marks)
a) exactly four are defective
b) Not more than four are defective.
Expert's answer
In the screws manufactured by a certain machine, 3 percent are found to be defective. If a
sample of 12 is taken, what is the probability that (5 Marks)
a) exactly four are defective

The probability that the screw is defective is 0.03. Then the probability that exactly four are defective is

P = (0.03)^4·(1-0.03)^(12-4) = 6.3483·10^(-7).

b) Not more than four are defective.

P = 1 - P(0 defective) - P(1 defective) - P(2 defective) - P(4 defective) =
& & = 1 - (0.03)^0·(1-0.03)^12 -
& - (0.03)^1·(1-0.03)^(12-1) -
& - (0.03)^2·(1-0.03)^(12-2) -
& - (0.03)^3·(1-0.03)^(12-3) -
& - (0.03)^4·(1-0.03)^(12-4) = 0.284.

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