3. Using the built in data set 'rivers': a. Create a histogram of rivers. This data set is skewed; calculate the skewness and comment on its value {i.e.: is it positive or negative skew). (10 pt] Create a distribution of sample means from rivers. Make each sample size = 5 and take 100,000 samples. You will need to do this in a for loop, and it may take a minute to run 100,000. Create a histogram of your distribution of sample means. Comment on the skewness of the distribution. (15 pt] Repeat (b), but this time with a sample size of 40. Again create a histogram and again comment on the skewness. Make sure you set the xaxis scale to be the same on all three histograms you've made (you may need to go back and rerun the prior hist( ) functions with additional arguments to ensure this). [15 pt) Describe what you see from the histograms of {a} - (c). Why are the distributions shaped differently? (5 pt) How does the standard deviation of the sample mean distribution (Le. the actual standard deviation you calculate from your specic runs of 100000 repeats] compare to the theoretical standard error of the mean ( l for 5 and 40 samples? (10 pt) 4. A city is studying the need for mass transit. One measure that the city is looking at is the current commute time for residents. The city planner has taken a random sample of 120 residents and found that the average commute time is 28.4 minutes with a standard deviation of 15.1. Calculate a 90% condence interval for the mean commute time within the city. (5 pt]