Manipulate[
sigma=Sqrt[n p (1-p)];
binomialstand=ListPlot[Table[{(k-n p)/sigma,sigma*PDF[BinomialDistribution[n,p],k]},{k,IntegerPart[n p-4 sigma],IntegerPart[n p+4sigma]}],Filling->Axis,PlotRange->All,Axes->{True,False}];
normal=Plot[PDF[NormalDistribution[0,1],x],{x,-4,4}];
Show[{binomialstand,normal}]
,{n,3,2000,1},{p,0.03,0.97}]