A Boeing 737-724, N13716, operated by Continental Airlines as Flight 875, was undamaged during an inadvertent encounter with turbulence while descending for an approach to Panama City, in the Republic of Panama. A passenger was seriously injured during the flight encounter with turbulence. There were no other reported injuries or damage to the airplane. Visual meteorological conditions prevailed at the time of the accident. The international flight originated from the Houston International Airport (IAH) at 1414 UTC, with Panama City as its final destination. The Captain requested and received deviations from the intended route of flight to avoid inclement weather along the route of flight when the flight encountered moderate turbulence for approximately 7 to 8 seconds during descent. The cabin seat belt sign was illuminated and the flight attendants had made several announcements regarding the seat belt sign when a passenger fractured his leg after he elected to leave his seat. The injured passenger was attended to by an on-board physician until he was de-planed by local paramedics.