chaverim-
I’m not sure I’m following you.
There are many different possible values for a “variance of between 1 second and 30 minutes”. (There are also many different possibilities for the mean between 1 second and 30 minutes.)
I would also need parameters for the number of calls. (Feel free to throw in a discrete distribution if you feel it will be a better fit for the data.)
Just out of curiosity- what is your math background?