MD80 CREW TRANSPOSED ASSIGNED RADIAL TO DEPART BYP. THEY WERE ASSIGNED THE 208 DEG RADIAL AND THEY STARTED TO FLY THE 280 DEG RADIAL. THIS BROUGHT THEM INTO CONFLICT WITH A PARACHUTE JUMP ACFT OPERATING 2000-3000 FT ABOVE THEM.

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APCHING BYP ON BYP STAR; APCH TOLD US TO TRACK 208 DEG RADIAL OUTBOUND TO AVOID SKYDIVING ACTIVITY. WE STARTED OUT ON THE 280 DEG RADIAL INSTEAD. FO NOTIFIED CAPT WHO THEN TURNED BACK L TOWARDS THE 208 DEG RADIAL. APCH TOLD US TO LOOK FOR THE JUMPER ACFT AND TOLD THE JUMPER ACFT TO HOLD THE JUMPERS. WE PASSED DIRECTLY UNDER THE JUMPER ACFT DURING OUR TURN BACK TO THE L. THE CONCERN IS THAT WHILE WE DID INDEED TURN THE WRONG WAY INITIALLY; OUR DEV FROM THE INTENDED GND TRACK WAS NOT GREAT. I ESTIMATE NO MORE THAN 3 MI SINCE WE DID NOT COMPLETE THE WRONG TURN; BUT ONLY STARTED INTO IT BEFORE CORRECTING BACK. THIS DOES NOT SEEM TO BE A GREAT PLACE TO DROP HUMAN BODIES RIGHT THROUGH THE NORMAL GND TRACK OF THE STAR TO A MAJOR ARPT. WE RECOMMEND DROPPING SKYDIVERS IN ANOTHER PART OF THE BIG OPEN STATE OF TEXAS; OR CHANGING THE ARR PATTERN OF ALL ACFT DURING JUMP ACTIVITY. AS A NOTE AIRLINE X BEHIND US WAS GIVEN THE SAME CLRNC AND TRANSPOSED THE DIGITS ON READBACK. 208 DEG RADIAL WAS READ BACK AS 280 DEG RADIAL. SUPPLEMENTAL INFO FROM ACN 403211: AFTER TURNING 20 DEGS THE COPLT CORRECTED ME AND I IMMEDIATELY TURNED BACK L TO INTERCEPT THE CORRECT 208 DEG RADIAL. ZFW THEN NOTIFIED A CESSNA JUMP PLANE TO HOLD OFF ON RELEASING HIS JUMPERS. WE PASSED DIRECTLY UNDER THE JUMP PLANE IN OUR TURN WITH 2000-3000 FT SEPARATION OR MORE. CERTAINLY FATIGUE: AFTER A LONG DAY AND EARLY SIGN-IN WAS A FACTOR IN MY SLOW BRAIN TRANSPOSING THOSE OUTBOUND RADIAL NUMBERS.