Run the code block below. Discuss the differences between the histograms of $`$x$`,`$y$`,$ and $`$z$`.$ How do they help us understand the Central Limit Theorem?

$```\{$r$\}$

# Run this code block

# For replicability

set.seed$(2123)$

# Draw $5,000$ random observations out of a uniform distribution from $0-1,000$

x $<-$ runif$(5000,$ min $=0,$ max $=1000)$

# Take a sample of size $30$ from x

y $<-$ sample$($x$,30)$

# Run a simulation:

samples $<-2000$

sample$\_$size $<-30$

z $<-$ vector$($length $=$ samples$)$

for$($i in seq$\_$along$($z$))\{$

z$[$i$]<-$ mean$($sample$($x$,$ sample$\_$size, replace $=$ TRUE$))$

$\}$

# Create histograms of x$,$ y$,$ and z

hist$($x$,$ freq $=$ FALSE, xlab $="")$

hist$($y$,$ freq $=$ FALSE, xlab $="")$

hist$($z$,$ freq $=$ FALSE, xlab $="")$