A workplace (call centre) has $n$ staff, $w_1, w_2, ..., w_n$ and the company requires $x$ amount of calls to be made for the week.
Let $x_1, x_2, ..., x_n$ be the percentage of calls (of the total calls$x$) that each worker is expected to complete for the week; so $x_1 + x_2 + ... + x_n = 100$
I am looking for the probability that worker $w_i$ completes the most calls in the week?
The number of calls that a worker makes can be assumed to follow a Poisson Distribution.
I'm not sure on the best strategy to tackle this? Do we create a Poisson distribution for each worker, and then look at the probabilities from each distribution and sum up the ones where worker $w_j$ ends up with the most calls?