It was believed that the probability of a small business that declared bankruptcy per month was the same in any month. Also the number of small businesses that declared bankruptcy was the same every month. Which of the following distributions would you use to determine the probability that more than three bankruptcies will occur next month?
A) binomial distribution
B) Poisson distribution
C) both of the above
D) none of the above

Question

Quizplus · Accepted Answer

The Poisson distribution is appropriate in situations where the events are rare, random, and independent of each other, such as the number of small businesses that declare bankruptcy per month. The binomial distribution is appropriate when the events have only two possible outcomes and are independent of each other, such as the number of heads or tails in a series of coin tosses. As the question assumes a constant probability of bankruptcy for each small business every month, the Poisson distribution fits the given scenario better than the binomial distribution. Therefore, the choice would be B - Poisson distribution.

It Was Believed That the Probability of a Small Business