- Create a sampling distribution given [latex]\mu[/latex] and [latex]n[/latex].
- Know and check the conditions of the Central Limit Theorem.
- Use the normal approximation to compute probabilities involving sample means when appropriate.
Sampling Distribution of a Sample Mean
A sampling distribution is the probability distribution of a sample statistic, such as a sample mean or sample proportion, as it varies from sample to sample. Let’s explore the sampling distribution of the sample mean for varying sample sizes and discover the Central Limit Theorem as it applies to means.