but I figure if someone knows how to answer it, it may be someone here.
Basically I have this weird distribution where the customer service agent speed (in terms of contacts per hour) is very strongly correlated with the % of priority emails answered.
Mind you, the priority emails are a different topic, and may, or may not, be easier or harder to answer.
I'm thinking I should hold off telling you which direction the correlation is, to not bias your judgement.
But I want to know if this distribution is due to cherry-picking emails ----- or a random phenomenon.
Let's say we have 5 agents who answer 20 emails/ hour, and 5 agents who answer 10 emails/ hour.
If 6% of emails are "high priority" and immediately flow to the top of the pile, and come in at random intervals (poisson distribution) ---- would the "fast" agents statistically answer a higher (% of their total) priority emails, equal %, or lower % than the "slow" agents?
Mind you the next email is only fed once the agent is done on the current one (duration of work twice as long for slow agent of course).
I know this is a complicated question but just throwing it out there. I'm kind of interested in how to tackle this, if not just somehow running a Monte Carlo simulation.