In statistics and probability theory, we can define probability distribution as a mathematical function or frequency distribution that shows the probabilities of the occurrence of various possible outcomes for an experiment. In other words, we can say that probability distribution is a mathematical illustration of a random phenomenon in terms of its sample space and the probabilities of events. There are different types of probability distributions, such as binomial, Poisson, normal, exponential, etc. Certain probability distributions occur in real-life situations which we may not observe. Let’s see some examples of probability distributions in real-life scenarios.
Below are some situations where we apply a binomial distribution, one of the probability distributions.
- The number of tails or heads appeared in a sequence of tossing a coin multiple times
- The number of male or female workers in a factory
- The number of defective or non-defective products in a certain amount quantity of products
- The number of successful exchanges of a company and so on
However, to use probability distribution techniques in real-life situations, one must be aware of some basic terms such as what is mean, what is standard deviation, what is z score, etc. These parameters will help in solving real-world problems using probability distribution methods.
Let’s consider a simple example to understand more about real-life applications of the probability distribution. Generally, many people arrive at the stadium to watch the game about the same time before the game starts. That would account for the majority of the crowd. If the game is significant, people arrive as early as possible. On the other hand, if it is a late-night game or the weather is bad, people may plan to arrive late. This situation can be effortlessly modelled with the help of normal probability distribution. By seeing how the stadium fills up, the association can employ simple normal probability distribution to determine when they should start selling upgraded tickets. Apart from this, there is no need to do data analysis.
We collect vast data and fit complex models to uncover exciting insights. In some circumstances, accumulating data itself is an expensive process. At times, we keep data only for the response variable. However, instead of spending a lot of time and effort gathering information, a simple approach like a probability distribution study can provide us with more insights into that particular problem.
Normal distribution illustrates statistics calculated from random data models or samples, as the central limit theorem specifies. We can apply normal distribution to random data collection samples to discover specific results. In this case, we can easily assume the normality of regression model errors or perform some hypothesis tests.
The Poisson distribution is one of the important types of distributions that arise in many business situations. It usually applies in cases where random events occur at a specific rate over time. For example, the number of customers visiting the bank in an hour, the number of defective products in a weekly production lot, the number of calls to specific customer care in a day, etc. There are many situations where we can apply probability distribution formulas in our daily lives.