What is the Central Limit Theorem Calculator?

The Central Limit Theorem Calculator is a statistical tool that helps users compute probabilities related to sample means when the population mean, population standard deviation, and sample size are known. Using the Central Limit Theorem, the calculator converts the sample mean into a Z-score and determines the probability of observing a value above, below, or on both sides of the given sample mean. This tool is essential for students, researchers, and analysts who want to understand how sample means behave and how likely certain outcomes are in repeated sampling.

How to Use:

1. Enter Population Mean (μ): Provide the true average of the population.
2. Enter Population Standard Deviation (σ): Input the spread of the population values.
3. Enter Sample Size (n): Specify the number of observations in your sample.
4. Enter Sample Mean (x̄): Enter the observed mean from your sample.
5. Select Tail Type: Choose right-tailed, left-tailed, or two-tailed probability.
6. Click “Calculate”: The calculator computes the standard error, Z-score, and resulting probability.
7. Review Result: The output displays all values clearly so you can easily interpret the sample mean’s statistical significance.