Part C: The following relate to an experiment in which you roll $n$ dice and calculate the

mean value. You repeat this experiment $m$ times.

C$1)$ Create a Matlab script in which $n$ and $m$ are each $100.$ Plot a histogram and a

normal probability plot of the sampling distribution. Does the sampling distribution

appear to be normally distributed? How can you tell? Plot a histogram of the underlying

distribution $($i$.$e$.$ rolling a die$).$ What is the distribution of the underlying process?

C$2)$ What is the effect of increasing or decreasing $n,$ the number of samples? What is

the effect of increasing or decreasing $m,$ the number of times the experiment is

run? Create a set of histograms that illustrate the effect of changing $n$ and $m.$

Matlab hints:

There are multiple ways to create solve this problem. I would create a nested

for loop where the outer loop is run $m$ times, and the inner loop is run $n$

Use the "normplot$()"$ function to create a normal probability plot. You can

either search for this function in the Matlab help or simply type "help

normplot" to get help on using this function.

The following code snippet may help you scale your histograms nicely.

histogram$($y$)$;

axis$([0\mathrm{.}5$ histogram$($y$).$Values$)])$