AN A320 FLT EXPERIENCES SEVERE TURB AT FL370 70 MI E OF THE TSTM ACTIVITY ON THE WESTERN SLOPES OF THE NORTHERN ROCKIES NEAR LKT; ID.

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WE HAD BEEN ALERTED BY CTR (EITHER ZSE OR ZLC) OF CONTINUOUS TO OCCASIONALLY MODERATE TURB FROM FL250-FL350. HE ALSO STATED THAT IT WAS SMOOTH AT FL370. WE REQUESTED FL370. BEFORE WE CLBED ABOVE FL250 I INSTRUCTED THE FLT ATTENDANTS TO REMAIN SEATED ALONG WITH AN ANNOUNCEMENT TO THE PAX TO STAY IN THEIR SEATS AND OBSERVE THE FASTEN SEATBELT SIGN; WHICH WAS ON. PRIOR TO DEPARTING SEATTLE; ENRTE TO MEMPHIS; I HAD CHKED THE WX ALONG OUR RTE OF FLT AND HAD PLOTTED ON A MAP 2 AREAS OF CONVECTIVE ACTIVITY THAT OUR COMPANY HAD ISSUED TO US. COVERAGE WAS 2/10 - 3/10 IN COVERAGE WITH TOPS FL330-FL360. AS WE WERE CLBING TO FL370; WE REMAINED WELL CLR OF THE WX AREAS 50-70 MI E OF THE WX. OUR RADAR WAS ON AND PAINTING THE WX W OF OUR POS; APPROX 70 MI W; TOPS FL330-FL360. CONVECTIVE ACTIVITY SHOWN ON OUR RADAR; LIGHT TO MODERATE RAINSHOWERS. WX LOCATED IN W TO W CENTRAL WASHINGTON. ON CLBOUT TO FL370; WE EXPERIENCED LIGHT TO OCCASIONAL MODERATE TURB. AS STATED BY THE CTLING CTR; FL370 WAS SMOOTH. I WAITED SEVERAL MINS AND THEN INSTRUCTED THE FLT ATTENDANTS TO START THEIR CABIN SVC. HOWEVER; THE SEATBELT SIGN REMAINED ON JUST AS A PRECAUTION. WE WERE 1500-2000 FT ABOVE ALL THE CLOUDS; UNLIMITED VISIBILITY IN THE CLR. THIS REMAINED SMOOTH FOR 10 MINS WHEN WE EXPERIENCED MODERATE TO SEVERE TURB FOR 30 SECONDS. MY FO TOLD THE FLT ATTENDANTS TO SIT DOWN. THE RIDE SMOOTHED COMPLETELY OUT AFTER 30-45 SECONDS AND REMAINED SO AT FL370. I FOUND OUT LATER ONE OF OUR FLT ATTENDANTS HAD BEEN INJURED. SHE FELL ON A BEVERAGE CART (INJURIES WERE NOT SERIOUS; SHE CONTINUED WORKING FOR THE WHOLE FLT 4 HRS). NO PAX WERE HURT. WE NOTIFIED OUR COMPANY DISPATCHER AND RPTED THE TURB AND FLT ATTENDANT INJURY. ALSO; AN ACFT INSPECTION WAS MADE AT MEMPHIS.