If your labor is moving so quickly that sitting you up for placement of an epidural for 15 minutes means the baby will be born during those 15 minutes.
If you have had a baby before, and you have a history of rapid transition. It will probably go fast again.
It all really depends on the situation and the person!
As you can see, there really is no "magical" number of dilation in any of my answers. I'm very sorry that I cannot give a definitive answer to this question. To put it very simply, each woman is different. Each labor is different.
Many, many women ask for an epidural or something for pain during transition, I have noticed in my 8+ years as an L&D nurse. Transition is hard, fast and furious for many women. This is when the pain really can intensify, and those inner feelings scream out "I can't do this anymore!!!" and "I need drugs!!!!". I know it's no consolation when you are in the throes of transition, but these responses are normal! Unfortunately, things might be moving too quickly to be able to get medication or an epidural by this point. It's not always the case, but sometimes it's true.
(This post was spurred by a recent birth with a multip who was moving too fast in her labor to get an epidural. 10 minutes after sitting her up higher in the bed, she birthed her baby - sans epidural.)