$1)$ follow the example to demonstrate central limit theorem with $1000$ row times $30$ variables, but this time use random variables with binomial distribution of p$=0\mathrm{.}5,$ n$=1.$ Let us call it X and X$-$bar. Create the similar statistics and generate the similar set of two histograms in the lecture. You need to adjust the bin size to optimize the look of the histograms. Post both histograms$$

$2)$ Can you tweak the excel sheet a little to convert this exercise into a computer simulation of the mechanical Galton machine? $($hint: just change the function of x$-$bar column from average to sum will do the trick, also the bin interval would be $0,1,2,3,...,30$ to simulate there are $31$ slots at the bottom. But think about why that is case.$)$ The difference is now we can increase the level and number of balls to a much larger number, and adjust p to any value. Try a few different parameter values. Explain why using sum function will do the trick and post a histogram that that shows a computer simulation of$$ the Galton machine.$$