Question

A large shipment of disposable flashlights contains 1% that are defective. Use the Poisson approximation of the binomial distribution to find the probability that among 200 flashlights randomly selected from the shipment: What is the parameter of the Poisson distribution in this scenario?

a) Mean (λ) = 1
b) Mean (λ) = 2
c) Mean (λ) = 3
d) Mean (λ) = 4

Answer 1

The parameter of the Poisson distribution in this scenario is Mean (λ) = 2.

Step-by-step explanation:

The parameter of the Poisson distribution in this scenario is option a) Mean (λ) = 1.

To find the parameter of the Poisson distribution, we use the mean of the binomial distribution. The mean (expected value) of a binomial distribution is given by λ = np, where n is the number of trials and p is the probability of success.

In this case, 1% of the flashlights are defective, so the probability of success is 0.01. The number of trials is 200. Therefore, the mean of the binomial distribution is λ = 200 * 0.01 = 2.

Therefore, the parameter of the Poisson distribution is Mean (λ) = 2, so option b) is the correct answer.