data := {{1, 0}, {2, 0}, {3, 1}, {4, 1}, {5, 5}, {6, 4}, {7, 11}, {8,
24}, {9, 18}, {10, 20}, {11, 9}, {12, 6}, {13, 0}, {14, 0}, {15,
1}, {16, 0}, {17, 0}, {18, 0}}

model[x_] = ampl Evaluate[PDF[NormalDistribution[x0, sigma], x]];
fit = FindFit[data, model[x], {ampl, x0, sigma}, x]
Show[ListPlot[data],
Plot[model[x] /. fit, {x, 0, 19}, PlotStyle -> Red],
AxesLabel -> {"# of Heads", "# of Trials"}]