# Central Limit Theorem and the Normal Distribution

This video describes the central limit theorem and some properties of the normal distribution. Understanding this will help you tie together many of the different types of hypothesis tests and confidence intervals that are used in statistics because they rely on something called the normal approximation. However, understanding the central limit theorem is not essential for a good understanding of statistics. It is an abstract idea so can be challenging. If you find it difficult, I suggest you move on and focus on the section that describes the normal distribution.

## Learning outcomes

On watching this video, students should be able to:

1. Explain why the normal distribution is so important for statistics.
2. Explain that the central limit theorem (CLT) is about the distribution of point estimates and that given certain conditions, this distribution will be nearly normal even if the sample data are non-normal.
3. Identify the conditions when the CLT can be used for inference involving a sample mean:
• The sample size is sufficiently large or the population is considered to have a normal distribution
• The observations in the sample are independent
4. Identify the conditions when the CLT can be applied for inference with a sample proportion:
• The sample is sufficiently large (guideline: np≥10 and n(1-p)≥10, where n = sample size and p=proportion of interest)
• The observations in the sample are independent
5. Describe how probabilities are extracted from the standard normal distribution and how these are used to construct confidence intervals and perform hypothesis tests.