Well first of all I have personally seen one in eastern N.C. between New Bern and Havelock in that big National Forest ( I forget the name). I talked to the Wildlife Resources Commission and at first they thought I was crazy, but they said that if I really saw one, it must have been one that was a pet and was released. That may be the case.
And second, you need to worry about more than your livestock. Those things kill people with some regularity out west. Most often juvenile male cats, attacking joggers. Seems they are not very experienced hunters, and they mistake you for a deer.
So, just to be safe, if you are a jogger, you may want to stick to the treadmill or the track down at the high school.