> For the complete documentation index, see [llms.txt](https://otd.gitbook.io/book/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://otd.gitbook.io/book/central-limit-theorem/central-limit-theorem-intro.md). # Overview The central limit theorem states that the averages of samples drawn from any distribution tend towards a normal distribution. This concept surfaces in many settings and you likely have some intuition for understanding this topic already! In science class, for instance, we often perform multiple trials of an experiment because reporting the average result over multiple trials is less error-prone than reporting the result of one trial. This module will introduce the formal statistics behind this concept and will show how this concept most frequently shows up in data science in the form of confidence intervals. The first section will cover discrete and continuous probability distributions. The second section will show examples of the central limit theorem in action. The third and final section will show how the central limit theorem allows us to construct confidence intervals. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://otd.gitbook.io/book/central-limit-theorem/central-limit-theorem-intro.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.