PRIOR TO INFLT TURB ENCOUNTER THE FLC HAD NOT BEEN BRIEFED BY DISPATCH OF POSSIBLE SEVERE WX; NOR WERE THERE VISUAL CLUES. BEFORE THEY REALIZED THEY WERE ENTERING A SEVERE WX AREA THEY HAD ALREADY EXPERIENCED SEVERE TURB AND PAX INJURIES. INJURIES WERE CAUSED BY PAX DISCONNECTING SEAT BELT AND OR WEARING IT TOO LOOSE.

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APPROX OVER MUNDO ENCOUNTERED OCCASIONAL LIGHT TURB AND SEAT BELT SIGN WAS TURNED ON. ANNOUNCEMENT MADE. SLIGHT HAZE LAYER WAS ENCOUNTERED AT THIS TIME. I CONTACTED ATC FOR RIDE RPTS AT FL350 BUT WAS PUT ON STANDBY. I THEN CONTACTED AN ACR FLT WHO HAD DSNDED FROM FL350 BECAUSE OF CONTINUOUS CHOP AT FL350. ABOUT 20 NM W OF MUNDO THE TURB INCREASED FROM LIGHT TO MODERATE TO SEVERE. WE ENCOUNTERED RAIN AND PROBABLY SOME HAIL -- SOME LIGHTNING WAS PRESENT IN THE AREA NO STRIKES WERE NOTICED. THE AUTOPLT KICKED OFF AND THE ACFT WAS HAND FLOWN BY THE FO. AN ATTEMPT TO CONTACT ATC WAS MADE TO NO AVAIL AND A TURN TO THE L WAS MADE TO EXIT THE UNEXPECTED WX. DURING THIS TIME WE LOST APPROX 500 FT. WE WERE AT FL310 AND DURATION WAS APPROX 15-25 SECONDS. PIREP ISSUED; DISPATCH NOTIFIED AND ATC NOTIFIED. I WAS LATER ADVISED THAT 3 PAX WERE REQUESTING A PARAMEDIC. 2 PAX; MR A AND MISS B; HAD RELEASED THEIR SEAT BELTS AND STOOD UP DURING THE FLT. ONE PAX; MISS C; WAS INJURED BECAUSE HER SEAT BELT WAS NOT TIGHT. ALL 3 WERE EXAMINED AND RELEASED AT THE ACFT. THEY WALKED OFF. NO FLC WERE INJURED AND WE CONTINUED TO MEXICO CITY FOR AN UNEVENTFUL LNDG. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR CAPT VERIFIED THE DATE BECAUSE THE DATE ON THE IDENT STRIP WAS IN ERROR. ALSO; THE ACFT TYPE WAS IDENTED AS B737-300. BECAUSE THE RPT REFERRED TO ALL INJURED PAX EXAMINED AND RELEASED AT THE ACFT -- AND THEN THE FLT CONTINUED TO MEXICO CITY. IN FACT; THE ACFT LANDED AT MEXICO CITY SOME TIME AFTER THE ENCOUNTER AND INJURIES. RPTR SAYS THAT THERE HAD BEEN A LARGE STORM IN THE GULF OF MEXICO WHICH APPEARED TO BE HEADING OUT OF THE FLT RTE; BUT THEN IT TURNED AND CAME BACK. THE RPTR'S COMPANY DISPATCH HAS THE CAPABILITY OF SEEING THE WX DISPLAY AS WELL AS THE POS AND TRACK OF THE ACFT; SO RPTR QUESTIONED DISPATCH AS TO WHY THEY DIDN'T ALERT THEM TO THE DEVELOPING BAD WX. THEY WERE ENTERING INTO AN AREA OF HAZE SO DIDN'T KNOW OF THE IMPENDING STORMS SO CONSEQUENTLY HAD NOT TURNED ON THE RADAR. AS SOON AS THE TURB WAS ENCOUNTERED THEY TURNED ON THE RADAR AND THE AREA WAS SOLID RED. RPTR BELIEVES THEY WERE IN THE MIDDLE OF THE 'ANVIL' OF A LARGE CUMULO NIMBUS. THE ACFT SUSTAINED SOME HAIL DAMAGE TO THE NOSE CONE AND RPTR HAD A REVIEW WITH HIS COMPANY. TWO OF THE PAX WHO WERE INJURED WERE A COUPLE; BUT HAD BEEN SITTING ON OPPOSITE SIDES OF THE ACFT APPARENTLY IN A FIGHT. AT THE FIRST TURB AND THE SEAT BELT SIGN TURNED ON; THE COUPLE DECIDED TO MAKE-UP AND RELEASED THEIR SEAT BELTS TO SIT TOGETHER. RPTR SAYS THAT THE OVERHEAD BAGGAGE BIN WAS ACTUALLY DENTED BY ONE OF THEIR HEADS HITTING IT. RPTR SAYS THAT DISPATCH NOW HAS THE CAPABILITY OF VIEWING WORLD-WIDE WX FROM SATELLITES AS WELL AS TRACKING THE ACFT ENRTE. ON ONE OCCASION RPTR WAS DEVIATING FOR WX WHEN HIS COMPANY DISPATCH CALLED HIM TO INFORM HIM THAT THE HEADING ON WHICH HE WAS DEVIATING WOULD TAKE HIM INTO ANOTHER AREA OF SEVERE WX.