Final answer:
The deer that fans out its white tail when disturbed and running is the White-tailed deer. They display this as a signal of alarm to other deer or potentially as a predator distraction technique.
Step-by-step explanation:
The deer that is known to fan out its tail when it is disturbed and running is the A. White-tailed deer. White-tailed deer are widely recognized by the characteristic white underside to their tail, which they display prominently when alarmed. By fanning out and raising their tail, they can communicate danger to other deer, as well as use the white flash coloration as a potential way to distract predators or signal their presence.