Question

It is known that 2% of the circuit boards from a production line are defective. If a random sample of 100 circuit boards is taken from this production line, use Poisson approximation to estimate the probability that the sample contains: a) exactly 3 defective boards, b) at least 3 defective boards

Answer 1

rate = 0.02

λ = rate*n = 0.02*100 = 2

a.

P(3) = e^(-2) * 2^3 / (3!)

= 0.1804

b.

P(k>=3) = 1 - P(0) - P(1) - P(2)

= 1 - [ e^(-2) * 2^0 / (0!) ] - [ e^(-2) * 2^1 / (1!) ] - [ e^(-2) * 2^2 / (2!) ]

= 0.3233

(please upvote)