307
• The population distribution of a variable is the distribution of its values for all members of the population.
• The sample mean of an SRS of size n drawn from a large population with mean μ and standard deviation σ has a sampling distribution with mean and standard deviation
The sample mean is an unbiased estimator of the population mean μ and is less variable than a single observation. The standard deviation decreases in proportion to the square root of the sample size n. This means that to reduce the standard deviation by a factor of C, we need to increase the sample size by a factor of C2.
• The central limit theorem states that, for large n, the sampling distribution of is approximately for any population with mean μ and finite standard deviation σ. This allows us to approximate probability calculations of using the Normal distribution.
• Linear combinations of independent Normal random variables have Normal distributions. In particular, if the population has a Normal distribution, so does .