Constructing Confidence Intervals

In the discussion for week 4, you rolled a pair of dice 10 times and calculated the average sum of your rolls.
Then you did the same thing with 20 rolls.
Use your results from the week 4 discussion for the average of 10 rolls and for the average of 20 rolls to construct a confidence interval for the true mean of the sum of a pair of dice (assume σ = 2.41).
What do you notice about the length of the interval for the mean of 10 rolls versus the mean of 20 rolls? Did you expect this? Why or why not?

Week 5 Discussion