I wrote this simple simulation:
There is a number of n nets in the ocean. Each net has a chance p of catching a fish every second. let's say the number of nets is 12 (n = 12) and the chance of catching exactly one fish is 50% every second. The resulting histogram is shaped like the bell curve after 10000 repeated simulation steps:
The mean is obviously 6 = n/2 if p is 50%
How can I derive the standard deviation from the knowledge i have? I don't want to mesure the process and find a good match. I want to find a solid formula for modelling the random distribution of how many fish go into the net any tick of the clock for variing p and n
Thanks in advance
The usual formula is $$S=\sqrt{\dfrac{1}{N-1}\sum_{i=1}^N\left(x_i-\overline{x}\,\right)^2}. $$ I would visually estimate the standard deviation to be (distance from mean to a point of inflection, since your distribution is approximately normal) approximately $2.5.$ Alternatively, if this is a binomial distribution, which it certainly appears to be, you can use the formula $S^2=npq=12(0.5)(0.5)=3,$ so that $S=\sqrt{3}.$ Here $q=1-p, \; p$ is the probability of "success", and $n=12$ is the number of trials.