Section 7.1 Summary

1. The sampling distribution of the sample mean for a given sample size consists of the collection of the means of all possible samples of size from the population. The mean of the sampling distribution of is the value of the population mean (Fact 1). The standard error is , where is the population standard deviation (Fact 2). For a normal population, the sampling distribution of is distributed as normal , where is the population mean and is the population standard deviation (Fact 3).
2. A simulation study showed that the sampling distribution of for a skewed population achieved approximate normality when reached 30. The Central Limit Theorem is one of the most important results in statistics and is stated as follows: given a population with mean and standard deviation , the sampling distribution of the sample mean becomes approximately normal as the sample size gets larger, regardless of the shape of the population.
3. We can use Facts 3 and 4 to find probabilities for problems involving sample means.
4. Similarly, we can find percentiles for the sample means.