This is really useful, but is this correct?

persons = 10~15 // → 10~15

budget = persons * 1~2 // → 12~27

Should it not say 10-30?

If they are truly independent of each other some of the uncertainty cancels out. 10 people and a budget of $1/person are both unlikely events, and two unlikely events occurring independently of each other is even more unlikely. And because the calculator is not about the full range of possible values but about the values in the 95% confidence interval this leads to the outer edges of the range now falling outside the 95% confidence interval