If you don't want to build a pegboard, you could also throw a bunch of coins and count how many heads you have. If you are running a pristine cocktail bar and want to avoid the subtle, discrete taste of approximation, you'd probably be able to find a physical process that gives you continuous, normal distributed values. Most physical processes do, after all.

Now, after that is settled, we just need to come up with a recipe...

Panel 1:
G and H are in a bar.
G: Ahh, finally going out for a drink again. I can’t wait to get so drunk that I regret to have started drinking in the first place.
Panel 2:
G: Oh, look! There’s a new cocktail on the menu. I love trying new stuff. Barkeep, give me a ... “Mixed Gaussian”!
H: looking at the menu What an odd name ...
Panel 3:
The barkeeper is putting a marble into a pegboard-like contraption
G: Whoa, what is all this? What are you doing? Aren’t you gonna make my cocktail?
H: Look at the menu!
Panel 4:
The menu reads: "The Mixed Gaussian - On average a good cocktail!"
Panel 5:
H: Sooo, how is it?
G: I guess it could be half a standard deviation sweeter but otherwise...
from off the panel: Ewwwww
Panel 6:
A duck is complaining to the barkeeper
D: Do you use a binomial distribution to make your Mixed Gaussian?! It tastes horribly like approximation! what kind of a bar is this?