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) Hypergeometric distribution.
D) None of the above.

Question

Quizplus · Accepted Answer

The scenario described is a classic example of the Poisson distribution, which models the number of occurrences of a rare event in a specified interval of time or space. The Poisson distribution assumes that the events are independent, occur at a constant rate, and have a low probability of occurring in any given interval. In this case, the bankruptcy of small businesses is a rare event, occurs independently of each other, and has a constant probability per month. Hence, the Poisson distribution is the most appropriate model to use for calculating the probability of more than three bankruptcies occurring next month. The binomial distribution assumes a fixed number of trials with a binary outcome, which is not applicable here. The hypergeometric distribution models the probability of drawing a specific combination of items from a finite population without replacement, which is also not relevant to this scenario.

It Was Believed That the Probability of a Small Business