Answer:
When the occurrence rate of defect is cut in half, the probability of a product having one or more defects drops drastically (0.0392 to 0.0198), to almost the half of its original value too.
Step-by-step explanation:
Poisson distribution formula
P(X=x) = f(x) = (λˣe^(-λ))/x!
λ = 0.04.
And the probability that a products one or more defects is the same thing as 1 minus the probability that a product has no defect.
P(X ≥ 1) = 1 - P(X = 0) = 1 - f(0)
P(X ≥ 1) = 1 - (0.04⁰e^(-0.04))/0! = 1 - 0.9608 = 0.0392
When the occurrence rate of defect is cut in half, that is, λ = 0.02,
P(X ≥ 1) = 1 - P(X = 0) = 1 - f(0)
P(X ≥ 1) = 1 - (0.02⁰e^(-0.02))/0! = 1 - 0.9802 = 0.0198
When the occurrence rate of defect is cut in half, the probability of a product having one or more defects drops drastically, to almost the half of its original value too.
Hope this helps!
