Seatbelt signs were illuminated—a sign in flight that it is safer to be seated and belted in—when an American Airlines 737-800 en route from New York to Miami encountered a passing storm system that caused turbulence severe enough to send 5 passengers and a flight attendant to the hospital. Pilots did not divert, but continued the flight to make a safe landing in Miami. Turbulence occurred forty minutes before landing. One flight attendant suffered a broken nose. 159 passengers were aboard the flight.