If your connecting flights happen on the same ticket, you will be guaranteed to arrive at your destination.
A ticket is a contract that says "we will transport you from point A to point B". In such connections, the delay is always calculated to allow you to easily change planes. If the inbound flight happens to be late, the airline will arrange the connection so that you can reach your destination, either by helping you transferring quicker or putting you on a later flight at no charge for you.
A story thet happened to me: I had to transfer at Atlanta coming from Paris. The transatlantic Air France flight was late. By the time we took to clear immigration and customs (the line was long), find our terminal and reach the gate, our connecting plane was already gone! I contacted the Delta Customer Care in the terminal; they promptly rebooked me on the next flight. This case has worked with two different airlines (Air France and Delta) as I had a through ticket.