Upvote:2
2 hours 50 minutes is plenty of time under normal conditions. As the numbers imply, terminals 7 and 8 are side-by-side, and catching the airtrain between terminals is (relatively) quick and easy.
Presuming you have booked both flights on a single ticket, if there are any problems that cause you to miss your connecting flight (flight delays, hold-ups in immigration, etc) then the airline will move you to a later flight at no charge.
Due to immigration and customs, all flights into the US require you to collect your bags at your first point of entry into the US. Thus in JFK you will need to collect your bags and take them though customs with you. Once through customs, if your bag has been tagged all the way to your destination (which it likely will have), you can simply drop it at the baggage drop point, and then make your way to terminal 8. If your bag has not been tagged all the way through to Nashville then you will need to take it to terminal 8 yourself.