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Manipulate[BarChart[Table[PDF[BinomialDistribution[n, p], i], {i, 0, 20}],
  PlotRange -> {{-.5, 21.5}, {-.1, 1}},
  Epilog -> {PointSize[0.03], RGBColor[1, 0, 0], Point[{n*p + 1, 0}]},
  ImageSize -> {450, 350}], 
  {{n, 10, "Variables"}, 1, 20, 1,Appearance -> "Labeled"}, 
  {{p, .5, "Skew"}, 0, 1, Appearance -> "Labeled"}]

Ladies and Gentlemen! How do I convert the binomial distribution inside this Manipulate (above) to a SmoothHistogram? Or, more simply put, where do I insert the term SmoothHistogram in this script?

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A few alternatives:

Using SmoothHistogram:

 Manipulate[ Module[{data = RandomVariate[BinomialDistribution[n, p], 500]}, 
   Show[Plot[PDF[BinomialDistribution[n, p], x], {x, 0, 20}, 
             PlotRange -> {{-.5, 21.5}, {-.1, 1}}, Evaluated -> True, 
             PlotStyle -> Directive[Thick, Blue], 
             Epilog -> {PointSize[0.03], RGBColor[1, 0, 0], 
             Point[{n*p + 1, 0}]}, ImageSize -> {450, 350}], 
        SmoothHistogram[data, PlotStyle -> Directive[Thick, Green]]]],
   {{n,  10, "Variables"}, 1, 20, 1,  Appearance -> "Labeled"},
   {{p, .5, "Skew"}, 0, 1, Appearance -> "Labeled"}]

enter image description here

Using SmoothKernelDistribution:

 Manipulate[Module[{data = RandomVariate[BinomialDistribution[n, p], 500]}, 
    Plot[{PDF[BinomialDistribution[n, p], x], 
          PDF[SmoothKernelDistribution[data], x]}, {x, 0, 20}, 
         PlotRange -> {{-.5, 21.5}, {-.1, 1}}, Evaluated -> True, 
         PlotStyle -> {Blue, Orange}, BaseStyle -> Thick, 
         Epilog -> {PointSize[0.03], RGBColor[1, 0, 0], Point[{n*p + 1, 0}]}, 
         ImageSize -> {450, 350}]], 
  {{n, 10, "Variables"}, 1, 20, 1, Appearance -> "Labeled"}, 
  {{p, .5, "Skew"}, 0, 1, Appearance -> "Labeled"}]

enter image description here

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