There is a population of four people: Amy, Brianna, Carlos, & Darius. [Note: this is a population, not a sample.] They are asked how many movies they saw last month. Amy saw 4 films, Brianna saw 10 films, Carlos saw 2 films, and Darius saw 4 films. We are too lazy to poll the entire population, so we take a sample of two (with replacement and order matters).

1. What is the probability that the mean of a randomly selected sample equals the mean of the population?

2. What is the probability that your error (the distance between what you want to know and your estimate of what you want to know) is two films or less? Explain how you know this.

3. If we increased the sample size to nine (instead of two), what would the standard error of the sampling distribution of the mean equal? Explain your work and how you got your answer please.