I have a work order system that serves the operational needs of a big organization. It has tickets and it gets completed in x days (0 < x < 1000) . I pulled out the data for completion time in days vs # of tickets. I plotted it and found out that this is exponentially distributed. I overlayed the exponential curve on top of the data and its a nice fit. I'm happy that it fits because now I can use the CDF & determine the probability of a new ticket getting completed within the deadline.
I have a hard time wrapping my head around it. My understanding of exponential distribution is "time between events in a poisson process". Why does this data fit in exponential distribution ? What would be the underlying poisson process ? Is there a rule of thumb to just look at the problem description and conclude its exponential ?