AN A320 FLT CREW TOOK OFF WITH EXCESSIVE TAILWIND COMPONENT BECAUSE THEY COPIED THE WIND DATA FROM THE TWR INCORRECTLY.

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TAXIING OUT FOR TKOF FROM JFK THE FO AND MYSELF DISCUSSED THE FACT THAT THE WX WAS DETERIORATING AND THE WIND WAS SHIFTING. ATC WAS BUSY; BUT NOT OUT OF THE ORDINARY. AS WE LINED UP FOR TKOF; AND COMPLETED THE BEFORE TKOF CHKLIST; ATC GAVE US A WX RPT; AND ASKED US IF WE WERE OK TO TAKE OFF. I WROTE DOWN THE WIND THAT I THOUGHT THAT I HAD HEARD ATC RPT; RESPONDED THAT WE WERE GOOD FOR TKOF; AND DEPARTED JFK. ON ARR AT PHX; I WAS ADVISED THAT I HAD DEPARTED WITH A 21 KT TAILWIND; WHICH IS OUTSIDE THE LIMITS OF THE AIRPLANE. THIS CONFOUNDED ME; AS I HAD WRITTEN DOWN THE WIND RPT THAT I HAD HEARD; WHICH WAS 210 DEGS AT 10 KTS. I THINK THAT ATC RPTED A WIND OF 010 DEGS AT 21 KTS; BUT I WROTE DOWN 210 DEGS AT 10 KTS. AS WE WERE DEPARTING RWY 22L AT JFK; 210 DEGS AT 10 KTS WOULD NOT BE OUT OF THE LIMITS OF THE AIRPLANE. OBVIOUSLY; 010 DEGS 21 KTS WOULD BE OUTSIDE THE LIMITS. THIS SITUATION WOULD NOT HAVE HAPPENED HAD I PAID CLOSER ATTN TO THE WIND RPT THAT ATC GAVE TO ME. ANY TIME YOU (I) ARE/AM ASKED BY ATC IF YOU (I) ARE/AM GOOD FOR TKOF; THIS SHOULD MAKE ME WONDER; 'WHY AM I BEING ASKED THAT?' UNFORTUNATELY; I HAD WRITTEN DOWN THE WRONG INFO; I THOUGHT THAT I WAS LEGAL FOR TKOF. I SIMPLY TRANSPOSED 2 NUMBERS; WHICH WAS A CRITICAL ERROR. MAYBE I DID THIS BECAUSE I WAS GIVEN THE INFO AS WE WERE COMPLETING THE CHKLIST. I DON'T KNOW. IN THE FUTURE; WHEN I AM ASKED IF I AM 'GOOD TO GO;' I WILL PAUSE; POSSIBLY ASK FOR MORE INFO; THEN ASSESS THE SITUATION. TRANSPOSING 2 NUMBERS IS A SMALL MISTAKE THAT COULD HAVE HUGE RAMIFICATIONS.