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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# Central Limit Theorem

By way of a quick review of the previous section, the law of large numbers tells us that as our sample gets larger, the closer our sample mean matches up with the population average. While this tells us what we should expect the value of the sample mean to be, it does not tell us anything at all about the distribution. For that, we need the central limit theorem. The central limit theorem (CLT) states that if we have a large enough sample size, the distribution of the sample mean is approximately normal, with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of n. This is important because not only do we know the typical value that our population mean can take, but we know the shape and variance of the distribution as well.

## Normal Distribution and the CLT

In Chapter 8, Foundational Probability Concepts and Their Applications, we looked at a type of continuous distribution known as normal...