Which of the following cannot generate a Poisson distribution?
A)The number of children watching a movie.
B)The number of telephone calls received by a switchboard in a specified time period.
C)The number of customers arriving at a petrol station on Christmas day.
D)The number of bacteria found in a cubic yard of soil.

Question

Quizplus · Accepted Answer

The Poisson distribution is used for modeling the number of times an event happens in a fixed interval of time or space under certain conditions (events occur independently, the average rate is constant, and two events cannot occur at the same time). The number of children watching a movie does not fit these criteria well because it is not about the occurrence of an event in a fixed interval in the same sense as the others. For example, the number of telephone calls or customers arriving fits the Poisson criteria because these can be counted per unit time, and each event (call or arrival) is independent of the others. The number of bacteria in a cubic yard of soil also fits because it's about occurrences in a fixed space. However, the number of children watching a movie is more about a total count at a given time rather than an event occurring repeatedly in a fixed interval.

Which of the Following Cannot Generate a Poisson Distribution