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 **
Defective rate = $2\% = 0.02$
Sample size = $100$
For Poisson approximation:
$\lambda = np = 100 \times 0.02 = 2$
Probability of exactly 2 defectives:
$P(X=2)=\frac{e^{-2}\,2^{2}}{2!}$
Given: $e^{-2}=0.135$
$P(X=2)=\frac{0.135 \times 4}{2}$
$P(X=2)=0.135 \times 2$
$P(X=2)=0.27$
Final Answer: $0.27$