In this lab, you will generate both Binomial and Normal observations, and simulate the convergence of the Binomial to the Normal for large n.

Set the seed to your 9-digit SID#:

set seed your_id

First, remind yourself what the normal approximation to a histogram might look like; generate 1000 standard normal observations:

set obs 1000
gen x = invnorm(uniform())

Make a histogram of the observations (use at least 10 bins) and superimpose a normal curve on the graph. (To superimpose a normal curve, use the norm option for graph: graph varname, bin(10) norm.) How well does the curve seem to approximate the histogram?

Now, generate 1000 observations of a binomial (n = 10, p = .5) random variable with the Stata command:

rndbin 1000 .5 10

This command produces a variable called xb. Make a histogram of the distribution with graph xb and assess how well the normal distribution fits.

Continue generating sets of 1000 binomials with p = .5, increasing n until the normal distribution provides a reasonably good approximation. How large an n did it take?

Now, generate 1000 observations of a binomial (n = 10, p= .2). Is the distribution of the observations well-approximated by the normal? Continue generating sets of 1000 binomials with p = .2, increasing n until the normal distribution provides a reasonably good approximation. How large an n did it take this time?

Now, generate 1000 observations of a binomial (n = 100, p= .01). Is the distribution of the observations well-approximated by the normal? Continue generating sets of 1000 binomials with p = .01, increasing n until the normal distribution provides a reasonably good approximation. How large an n did it take this time?