Comparing Binomial and Poisson Distributions

approxGraph[n_, p_,maxX_,maxY_]:=Show[
ListPlot[
Table[PDF[BinomialDistribution[n,p],x], {x,0,n}],
PlotStyle->{PointSize[.02],Red},
PlotRange->{{0,maxX},{0,maxY}}   ],
ListPlot[
Table[PDF[PoissonDistribution[n*p],x],{x,0,n}],
PlotStyle->{PointSize[.018],Blue},
PlotRange->{{0,maxX},{0,maxY}}],
PlotLabel->StringJoin["n=",ToString[n],", p=",ToString[p]]
];

approxGraph[20,.4,20,.5]

Manipulate[approxGraph[n,.2,40,.5],{n,5,100,10}]

n=20;p=.4;
Print["n = ",n,".    p = ",p,"     μ = ",n*p,
"     σ Bin = ",(Sqrt[n*p*(1-p)]),
"     σ Poi = ",(Sqrt[n*p])]
TableForm[Table[
{x,PDF[BinomialDistribution[n,p],x],
PDF[PoissonDistribution[n*p],x]},
{x,0,n}]]
Clear[n,p]

n=200;p=.4;
Print["n = ",n,".    p = ",p,"     μ = ",n*p,
"     σ Bin = ",(Sqrt[n*p*(1-p)]),
"     σ Poi = ",(Sqrt[n*p])]
TableForm[Table[
{x,PDF[BinomialDistribution[n,p],x],
PDF[PoissonDistribution[n*p],x],PDF[BinomialDistribution[n,p],x]-
PDF[PoissonDistribution[n*p],x]},
{x,0,n,10}]]
Clear[n,p]

n=100;p=.4;
Print["n = ",n,".    p = ",p,"     μ = ",n*p,
"     σ Bin = ",(Sqrt[n*p*(1-p)]),
"     σ Poi = ",(Sqrt[n*p])]
TableForm[Table[
{x,PDF[BinomialDistribution[n,p],x],
PDF[PoissonDistribution[n*p],x],PDF[BinomialDistribution[n,p],x]-
PDF[PoissonDistribution[n*p],x]},
{x,0,n,5}]]
Clear[n,p]