There are too many variables for a question like this to be realistic. Lets be specific, is the deer running full speed, flat or bounding, how many deer are there, is it open woods, a cutover, a field, what is the weapon, the distance, and on and on and on and on.
There's a single doe running across an alfalfa field at 65yards and you have a shotgun. She's heading towards some thickets and you have about 10 seconds from the time you see her untill the time she has made it to the woods