The Central Limit Theorem Quiz

1. A population has mean $20$ and variance $9$. For samples of size $36$, what is the approximate distribution of $\bar{X}$?

• A. $\mathrm{N}(20,\,9)$
• B. $\mathrm{N}(20,\,0.25)$
• C. $\mathrm{N}(20,\,0.5)$
• D. $\mathrm{N}(20,\,324)$

2. $X\sim\mathrm{Geo}(0.25)$ and $n=48$. What is $\mathrm{Var}(\bar{X})$?

• A. $0.25$
• B. $12$
• C. $4$
• D. $0.5$

3. Which statement about the CLT is correct?

• A. It only works for normal populations.
• B. It shows a single observation is approximately normal.
• C. It shows the sample mean is approximately normal for large samples.
• D. It requires the sample size to be less than 30.

4. $X\sim\mathrm{B}(20,0.5)$ and $n=45$. What is the standard deviation of $\bar{X}$?

• A. $5$
• B. $0.745$
• C. $0.0556$
• D. $0.333$

5. If the sample size is increased, what happens to the standard deviation of $\bar{X}$?

• A. It increases
• B. It stays the same
• C. It decreases
• D. It becomes zero