I have values for minimum amount (a), middle amount (b), maximum amount (c), and a total count (Z). What I want to do is calculate the average amount (d) over that total min/mid/max spread, but with a cubic bezier curve (I think?) to spread the amounts around a kind of organic/non-linear representative range.
I don't have a math background (aside from programming), so I'm unsure of existing methods to spread the values over a range/max amount, nor how to adequately describe the problem.
An illustrated example: I have a $200$ events (Z), which can have between $10-2000$ attendees for each event (a-c). I want to weigh the middle point to the lower side, so I'll put it at $500$ (b).
$a = 10$
$b = 500$
$c = 2000$
$Z = 200$
Using the weighted bell curve, what would the average amount of attendees be to all the events?
Edit:
Based on JeanMarie's lead I looked into probability distribution.
I found something online which lead me to use this equation (sorry, I don't really know Math LaTeX notation):
$d = (a * Pa) + (b * Pb) + (c * Pc)$
$Pa$, $Pb$, $Pc$ equals the probability of each placement along the range. An applied example using the events as specified above (with estimated probability amounts) could be:
$d = (10 * 0.2) + (500 * 0.6) + (2000 * 0.2) = 702$
While this equation I can estimate a rough $d$ value, I don't feel it's entirely along the gauss/normalised distribution curve accounting for the variation/deviation in between. Is there a layman's equation that's a little more detailed to solve this?