CLT Practice

Practice Problems

Instructions

Answer the following questions, render the document and submit the .html report.

Questions

Suppose you take a sample of size $n=5$ from a right skewed distribution with a population mean, $\mu =125$ and a standard deviation, $\sigma =12$

Question: What is the mean of the distribution of sample means (${\mu }_{\overline{x}}$)?
Answer:

Question: What is the standard deviation of sample means (${\sigma }_{\overline{x}}$)?
Answer:

Question: What is the shape of the distribution of sample means and why?
Answer:

Now suppose you increase the sample size to $n=100$. What is:

Mean of sample means:
Standard deviation of sample means:
Shape of the distribution of sample means:

Describe the difference between the Law of Large Numbers and the Central Limit Theorem.
Answer: