This topic introduces the basic concept of Central Limit Theorem.

Lesson 1 of 3: Learning Outcomes

At the end of this lesson, you should be able to:

1. Calculate probabilities involving the sample mean by using the central limit theorem.
2. Apply probabilities of the sample mean values in real-life business problems by applying concepts on the sampling distribution of sample means.

Lesson 2 of 3: Central Limit Theorem (30 mins)

What is Central Limit Theorem (CLT)?

The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30. All this is saying is that as you take more samples, especially large ones, your graph of the sample means will look more like a normal distribution.

Additional Resources

Below video explains what Central Limit Theorem is all about.

https://youtu.be/YAlJCEDH2uY

Significance of Central Limit Theorem (CLT)

• The CLT permits us to use sample statistics to make inferences about population parameters without knowing anything about the shape of the probability distribution of the population.
• If we repeatedly take sufficient large samples from the population, the resulting sampling distribution will follow an approximately normally distribution.

Summary of Central Limit Theorem (CLT)

Refer to below diagrams. We can see that even though the population distribution is not normal, if the sample size n is greater or equal to 30,  we can apply the CLT to compute the sample mean using the above formula.

Example