AP Statistics / Unit 2: Probability, Random Variables, and Probability Distributions
2.12 Sampling Distributions and the Central Limit Theorem
Notes
A sampling distribution is the distribution of a statistic over all possible samples.
- Central Limit Theorem: for large $n$ (often $n\ge30$), the sampling distribution of $\bar x$ is approximately normal, whatever the population's shape.
Practice
The CLT is about the shape of:
It's about a statistic's distribution.
A population is strongly skewed. With samples of size 50, the distribution of $\bar x$ is:
The CLT applies for large $n$.
As $n$ increases, the spread of the sampling distribution of $\bar x$:
$\displaystyle \sigma_{\bar x}=\frac{\sigma}{\sqrt n}$.
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