What is the definition of a theoretical distribution that is often approximated in real-world situations and is symmetrical and bell-shaped?

The normal distribution is a fundamental concept in statistics, widely recognized for its characteristic symmetrical and bell-shaped curve. This distribution is significant in various fields because many natural phenomena tend to follow this pattern when appropriately aggregated or when the underlying processes are influenced by numerous small, independent factors.

The properties of the normal distribution include a mean (average) which is located at the center of the distribution, along with standard deviations that measure the spread of data around the mean. In practical applications, the normal distribution serves as a crucial tool for inferential statistics, allowing statisticians to make predictions and understand probabilities concerning data that tends to cluster around the mean.

This theoretical distribution is often used to approximate real-world data, especially when the underlying data set adheres to the Central Limit Theorem, which states that the distribution of the sample means will approach a normal distribution as the sample size becomes larger. Consequently, normal distribution provides a practical framework for various statistical analyses, hypothesis testing, and confidence interval construction.

Understanding the normal distribution is essential in statistics, as it lays the groundwork for more complex analyses and modeling techniques. In contrast, the other options do not pertain to a symmetrical and bell-shaped theoretical distribution: stratified sampling relates to a method for collecting samples, standard