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 $e^{-2}=0.135$]

0.27

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: $0.27$