What is the difference between Binomial, Poisson and Normal distribution? Give examples of real-life data apply to these three distributions.
The Correct Answer and Explanation is:
The Binomial, Poisson, and Normal distributions are all important in statistics, but they describe different types of data and situations. Here’s a breakdown of each:
- Binomial Distribution:
- Definition: The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure).
- Example: Tossing a coin 10 times and counting the number of heads. Each toss is independent, and the probability of getting heads on each toss is 0.5.
- Real-life data: A factory worker checks 100 products for defects. The number of defective products follows a binomial distribution if each product has a fixed probability of being defective, and the products are inspected independently.
- Poisson Distribution:
- Definition: The Poisson distribution describes the number of events occurring in a fixed interval of time or space when the events are independent and happen at a constant average rate.
- Example: The number of cars passing through a toll booth in one hour. The events (cars passing) are random, but they occur at an average rate.
- Real-life data: The number of customer arrivals at a call center in a given time period can often be modeled by a Poisson distribution, especially if calls are random and occur independently.
- Normal Distribution:
- Definition: The normal distribution, also called the Gaussian distribution, is a continuous probability distribution characterized by a bell-shaped curve. It is defined by its mean (average) and standard deviation (spread).
- Example: The distribution of people’s heights in a population. Most people are close to the average height, and fewer people are at the extremes (either very short or very tall).
- Real-life data: Test scores in a large population typically follow a normal distribution, with most students scoring around the mean, and fewer students scoring extremely high or low.
In summary:
- Binomial is used for discrete events with two outcomes in fixed trials.
- Poisson is used for the number of events in a fixed interval of time or space.
- Normal is used for continuous data that tends to follow a symmetric distribution around the mean.
Each distribution has its own conditions and applications in real-life data analysis.
