Show[
DiscretePlot[PDF[BinomialDistribution[1000,1/6],x],{x,100,250},PlotRange->All],
Plot[PDF[NormalDistribution[1000/6,(Sqrt[1000*5/36])],x],{x,100,250},PlotStyle->Orange]
]

Plot[PDF[NormalDistribution[1000/6,(Sqrt[1000*5/36])],x],{x,100,250},PlotStyle->Orange]

DiscretePlot[PDF[BinomialDistribution[1000,1/200],x],{x,0,100},PlotRange->All]