Could you explain a probability distribution that is not normal? Further, can you shed some light on a real-life scenario where this could be utilized?

Question Analysis

The question asks you to explain a probability distribution that is not the normal distribution (Gaussian distribution). This involves describing the characteristics and properties of another type of distribution. Additionally, you need to provide a real-life example where this non-normal distribution is applicable. The interviewer is testing your understanding of various statistical distributions and your ability to apply theoretical knowledge to practical situations.

Answer

One example of a probability distribution that is not normal is the Poisson distribution.

Characteristics of the Poisson Distribution:

• It is used to model the number of events that occur within a fixed interval of time or space.
• The events are independent, meaning the occurrence of one event does not affect the probability of another event occurring.
• It is characterized by a single parameter, (\lambda) (lambda), which is the average number of events in the given interval.

Real-life Scenario:
A practical example of the Poisson distribution is modeling the number of customer arrivals at a bank within an hour. If a bank manager knows that on average 10 customers arrive per hour, they can use the Poisson distribution to predict the probability of different numbers of arrivals in any given hour. This information can help in optimizing staffing and resource allocation to improve customer service efficiency.

By understanding and applying the Poisson distribution, organizations can make informed decisions based on the likelihood of various outcomes in situations where events occur randomly over a continuous time or space interval.