# 6.E: Sampling Distributions (Exercises)

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang.

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

### Basic

#### Q6.1.1

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.

#### Q6.1.2

Random samples of size $$64$$ are drawn from a population with mean $$32$$ and standard deviation $$5$$. Find the mean and standard deviation of the sample mean.

#### Q6.1.3

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

1. Random samples of size $$121$$ are taken. Find the mean and standard deviation of the sample mean.
2. How would the answers to part (a) change if the size of the samples were $$400$$ instead of $$121$$?

#### Q6.1.4

A population has mean $$5.75$$ and standard deviation $$1.02$$.

1. Random samples of size $$81$$ are taken. Find the mean and standard deviation of the sample mean.
2. How would the answers to part (a) change if the size of the samples were $$25$$ instead of $$81$$?

#### S6.1.1

$$\mu _{\bar{X}}=100,\; \sigma _{\bar{X}}=1.33$$

#### S6.1.3

1. $$\mu _{\bar{X}}=75,\; \sigma _{\bar{X}}=1.09$$
2. $$\mu _{\bar{X}}$$ stays the same but