I am writing my thesis and i have draw a hypothetical curve. Later I have to relate this with simulated data. The picture has a quadratic equation and some sample points are drawn. Now i have to draw a bell curve on each data points to show that their mean lies on the curve or they stay within the deviation. How do I draw that? Is it even possible to draw something like this. I am sorry, i already left the lab and couldn't bring the code related to the picture. Any help or guidance is really appreciated. Please also let me know if the question is not clear. I am also stumbling on making my expectation clear. Thanks in advance.

Hope this sheds some light.