# Raising the normal distribution curve to a specified height on the $y$-axis

I'd like to know how to fit the normal distribution curve between $$x$$ and $$y$$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I suspected.

The following is my Mathematica code where I tried to get the maximum to be $$y = 15$$ at $$x = 0$$. I also want $$x$$ to range over $$0,\, 1,\,\ldots, 100$$. I have started the plot from -50 to get the whole shape of the curve.

With[{sigma = 15, mu = 0},
t = Table[E^(-(x - mu)^2/(2 sigma^2)), {x, -50, 50}];
ListPlot[t #& @ #[t]& /@ {Mean, Variance, Median},
PlotRange -> Full, Filling -> Bottom]]


I thought that I could use median, or variance, or mean values to lift the curve up to 15, but it didn't work as I expected.

Can you help modify the code so that the curve will reach $$y = 15$$ rather than $$y \sim 0.38$$ and still keep the shape of a normal distribution curve?

Below is the image of the plots from the code above. With[{sigma = 15, mu = 0},
t = Table[E^(-(x - mu)^2/(2 sigma^2)), {x, -50, 50}];
ListPlot[# Rescale[t] & /@ {5, 10, 15}, PlotRange -> Full,
Filling -> Bottom, DataRange -> {-50, 50}]] Alternatively,

With[{sigma = 15, mu = 0},
t = Table[{x, E^(-(x - mu)^2/(2 sigma^2))}, {x, -50, 50}];
ListPlot[ScalingTransform[{1, #}][t] & /@ {5, 10, 15},
PlotRange -> All, Filling -> Bottom ]] 