g[n_,p_,x_]:=Module[{j},j=Round[n p + x Sqrt[n p (1 - p)]]; Binomial[n,j] p^j  (1-p)^(n-j)];
ϕ[x_]:=Exp[-x^2/2]/Sqrt[2 Pi ]

Plot[{ϕ[x],g[30,0.3,x]},{x,-5,5},Filling->{2->Bottom},PlotRange->All,PlotLegends->"Expressions"]