Answer to Question #273695 in Statistics and Probability for AMA

Question

Find the probability that at most 5 defective bolts will be found in a box of 200 bolts if it is known that 2 per cent of such bolts are expected to be defective. (you may take the distribution to be Poisson)

Answer 1

The appropriate distribution for this question is Poisson distribution.

$P(X=k) = \frac{λ^k \times e^{-λ}}{k!}$

Mean $λ= 200 \times 0.02 = 4$

P(X≤5) = P(X=0) + P(X=1) +...+P(X=4) + P(X=5)

By Excel function

P(X≤5) = POISSON(5,4,1)

P(X≤5) = 0.7851