Turn in one copy for each group. If group members are not present in class they will be required to complete their own lab to receive credit. Please turn in **both a DOC or PDF file and your R Markdown script**. This is due by the end of the day on Thursday, March 2. Groups *may* be asked to talk about their results in class.

Answer the following questions in this R Markdown document. Please include code where necessary.

The central limit theorem is a foundational idea in statistical inference. Typically, it is assumed that the mean of a sample converges to a normal distribution when the sample size is greater than (20 or 30?). So where do these numbers come from?

To look at this question, modify the function to also print a histrogram. For full credit your function should have appropriate titles, labels, and be aesthetically pleasing.

```
CLT <- function(num.sims){
# function that simulates uniform random numbers to illustrate the central limit theorem
# ARGS: num.sims - the number of samples to average in central limit theorem
# RETURNS: list containing the mean and standard deviation of the average of the samples
# SHOULD ALSO CREATE A HISTOGRAM, WITH APPROPRIATE TITLES
num.replicates <- 10000 # how many times to repeat this process
samples <- rep(0, num.replicates)
for (i in 1:num.replicates){
samples[i] <- mean(runif(num.sims, min = 0, max = 100))
}
# CREATE HISTOGRAM HERE
return(list(mean(samples), sd(samples)))
}
```

Demonstrate the function works by calling the function with 10, 30, 100, and 1000 samples. Briefly discuss the differences in these figures/results.

Download the data set on earthquakes, provided by the USGS, available at http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/EarthquakesAll.csv. The data set contains earthquakes from 1965 to 2016.

Create a compelling graphic from this data set. The choice of what and how is completely up to you. Then provide a short summary of the story your graphic depicts.