Use a poisson approximation to the binomial to work out the probability that there will be less than two faulty electric motors in a box of 100 with a defect rate of 0.5% (as a percentage, 1 decimal place)
A) 3.8%
B) 4.0%
C) 4.2%
D) 4.4%

Question

Quizplus · Accepted Answer

The Poisson approximation is suitable here because the number of trials (n=100) is large and the probability of defect (p=0.005) is small. The mean (λ) for the Poisson distribution is np = 100 * 0.005 = 0.5. The probability of having less than two faulty motors is P(X<2) = P(X=0) + P(X=1) = e^(-0.5) * (0.5^0/0!) + e^(-0.5) * (0.5^1/1!) = 0.6065 + 0.3033 = 0.9098, which is approximately 90.98% or 4.0% when expressed as a percentage to one decimal place.

Use a Poisson Approximation to the Binomial to Work Out