## The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean

This section gives several concrete examples of calculating the exact distributions of the sample mean. The corresponding means and standard deviations are computed for demonstration based on these distributions. Next, it discusses sampling distributions of sample means when the sample size is large. It also considers the case when the population is normal. Finally, it uses the central limit theorem for large sample approximations.

### The Mean and Standard Deviation of the Sample Mean

#### Exercises

1. Random samples of size $225$ are drawn from a population with mean $100$ and standard deviation $20$. Find the mean and standard deviation of the sample mean.

3. A population has mean $75$ and standard deviation $12$.

a. Random samples of size $121$ are taken. Find the mean and standard deviation of the sample mean.

b. How would the answers to part (a) change if the size of the samples were $400$ instead of $121$?