Question

Assume that there are 30 faulty products in a lot of 300 on average. If a shipment of 100 is going to be made, what is the probability that there will be exactly 3 of these products in this shipment?

Answer 1

The average is 30 faulty products in a lot of 300, thus the average is 10 per 100 products.

λ = 10

Formula Poisson probability:

$P(X=k) = \frac{λ^ke^{-λ}}{k!}$

Evaluate at k=3:

$P(X=3) = \frac{10^3 \times e^{-10}}{3!} \\ = \frac{1000 \times 4.539 \times 10^{-5}}{6} \\ = 0.0075$