How to generate a Gaussian curve using 2 user inputted values?

I am trying to plot a Gaussian curve for 1 day using 2 points named basepoint and peak. Both the basepoint and peak are to be taken as user input and based on those values a curve has to be generated with the peak value occurring at 14:00h.

The curve must start with the basepoint value and end again at the basepoint value with the numbers between the basepoint and peak being some randomly generated numbers

Is there a way this can be done?