With Python, how could I sample a randomly generated data-set to fit a theoretical distribution?

Here is a general example of what I did...

1. Start with a physical model of y=m*x + b
2. Generate uniform distributions of m, x, and b
3. Created a theoretical distribution of y by specifying y_average and y_standard deviation

The next step is to sample from the data that I randomly generated in (step 2) to obtain the combinations of m, x, and b that fit my theoretical distribution that I created in (step 3).

Below is a picture showing what I would like to do... I have the top graph, and I have created the theoretical distribution line in the bottom graph... I want to create the "blue bars" in the bottom graph using the top graph and the theoretical distribution line