What's a simple formula I can use for calculating the probability of a set of random numbers adding up to or being greater than another number? Where $W$ is the amount of random numbers picked, $X$ is the lower limit, $Y$ is the upper limit and $Z$ is the number I need to reach.
Example 1: 2 numbers are picked randomly from 500 to 800, what is the probability they will total 1300 or greater.
Example 2: 3 numbers are picked randomly from 400 to 600, what is the probability they will total 1500 or greater.
The random numbers can include the upper and lower limit and will only be whole numbers.
Edit 1: I should also add the exact same number can be picked multiple times (so they are replaced) and that any number is equally as likely as another.
Edit 2: Could the formula be any of these?
Do any of those work? If not, why not?