Equation for bell-shaped curve

I would like to create an equation for a smooth bell-shaped curve.

I have a dataset where because of some integer values in the data acquisition process there are actually two smaller 'humps' in the resulting graph instead of a normal smooth bell-shaped curve. Also, the extremes are missing due to lack of data.

So far, I can calculate a standard deviation and mean, but how can I convert this into an expression that would produce a smooth plot including the [interpolated] extremes?

Thanks