On May 16, 2009, at 1145 eastern daylight time, a Boeing 757-232, N657DL, operating as Delta Airlines flight 687, encountered turbulence while in cruise flight over Cuba. One passenger was seriously injured, and two passengers and two flight attendants sustained minor injuries. The captain, first officer, 2 flight attendants, and 180 passengers were not injured, and the airplane was not damaged. The flight was operating on an instrument flight rules flight plan under the provisions of Title 14, Code of Federal Regulations (CFR) Part 121. Instrument meteorological conditions prevailed in the vicinity of the turbulence. The flight departed from Hartsville Jackson International Airport (KATL), Atlanta, Georgia, at 1052, and was en route to Owen Roberts International Airport (MWCR), George Town, Cayman Islands. According to the captain, the airplane was at flight level 350, with the autopilot engaged, about 35 to 40 minutes from MWCR in Cuban airspace. He had turned the seat belt light on 5 to 10 minutes earlier, and the first officer had made the public address announcement that everyone needed to remain seated with their seatbelts fastened. The airplane was in a haze layer, the radar was on and painted only small patches of green, no yellow or red was showing, and there were no buildups up ahead. All of a sudden, the “ride” became severe, as the airplane climbed rapidly, to approximately 500 feet above the assigned altitude, and the autopilot disengaged. The captain took control of the yoke to stop the climb and slowly lowered the nose. As he was trying to level the airplane, it then pitched down, and was recovered about 500 feet below cruise altitude. The first officer attempted to communicate the event to the Cuban controller but language difficulties intervened. The captain stated that the event probably lasted about a minute, or slightly longer. The first officer called the cabin to assess any injuries; he was informed by a flight attendant that at least two, and perhaps three passengers appeared to be injured, as well as a flight attendant who had hurt her wrist and shoulder. The captain contacted the destination controller and requested that medical personnel meet the flight. Three passengers were transported to the local hospital for assessment. The flight attendant declined further treatment until returning to Atlanta. The lead flight attendant confirmed that the seat belt light had been on when the turbulence occurred.