Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given \(e^{-2}=0.135\)]
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.27
The number of defective bolts in a sample of n = 100 with p = 0.02 follows a Poisson distribution with mean
\( \lambda = np = 100 \times 0.02 = 2 \)
\( \displaystyle P(X = 2) = \frac{e^{-\lambda}\lambda^2}{2!} \)
\( \displaystyle = \frac{0.135 \times 4}{2} = 0.27 \)