STT 212 Lecture Notes - Lecture 11: Central Limit Theorem, Standard Deviation, Sampling Distribution
16 Apr 2019
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Document Summary
The central limit theorem is exactly what the shape of the distribution of means will be when we draw repeated samples from a given population. Specifically, as the sample sizes get larger, the distribution of means calculated from repeated sampling will approach normality. As the sample size increases, the sampling distribution of the mean, x-bar, can be approximated by a normal distribution with mean and standard deviation / n where: Is the population mean is the population standard deviation n is the sample size. In other words, if we repeatedly take independent random samples of size n from any population, then when n is large, the distribution of the sample means will approach a normal distribution. Suppose we draw a random sample of size n ( x1, x2, x3, xn 1, xn ) from a population random variable that is distributed with mean and standard deviation .
