A CRJ 200 CREW PROGRAMMED THE FMS FOR CVG 36L AND MISSED ATC'S RWY 36R ASSIGNMENT. AFTER THE CREW ASKED FOR WX DEVIATIONS TO RWY 36L THEY WERE VECTORED FOR ANOTHER APCH AND 36R FMS SETUP.

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I WAS THE PF; WE WERE TRANSITIONING THROUGH ROUGH WX AND DISCUSSING AN ALTERNATE RTE AROUND THE WX. ATC (CTR) SWITCHED US OVER TO CINCY APCH. THEY ASSIGNED US RWY 36R AND 10 DEGS TO THE L (WE WERE 17 MI FROM SNPPR). WITH THE WX; RAIN; TURB; I BELIEVE THAT THE 10 DEGS TO THE L WAS MISHEARD AS RWY 36L; WE CONTINUED IN AND AS APCH GAVE US FINAL VECTORS AND CLRED US FOR RWY 36R APCH WE REALIZED THAT SOMEONE HAD MADE A MISTAKE. WE QUERIED ATC; THEY GAVE US CLBING VECTORS TO THE E; WITH VECTORS FOR RWY 36R. WE BRIEFED EACH APCH TO ACR STANDARDS. WE RETURNED TO LAND WITH NO OTHER ISSUES. SUPPLEMENTAL INFO FROM ACN 750641: JUST AFTER CHKING IN WITH APCH IN CVG WE REQUESTED VECTORS TO THE L OF COURSE FOR WX. I LOADED RWY 36L IN THE FMS AND BRIEFED APCH PLATE AND SWITCHED TO FINAL CTLR. WE DID NOT CONFIRM THE RWY ASSIGNMENT. WE WERE VECTORED TO RWY 36R. WE WERE NOT SET UP FOR RWY 36R AND NOTIFIED THE CTLR WE HAD BEEN ASSIGNED THE L SIDE. HE VECTORED US TO THE R AND BACK AROUND FOR RWY 36R OUTSIDE OF SNPPR. WE HAD RE-SETUP FOR RWY 36R AND BRIEFED AS APPROPRIATE. I SPOKE WITH ATC AFTER ARR INTO CVG AND WAS TOLD OUR INITIAL ASSIGNMENT WAS RWY 36R AND L DEVS AFTER THE ASSIGNMENT WAS GIVEN WERE ISSUED. THE CTLR THOUGHT THAT MAY HAVE CAUSED SOME CONFUSION. HOWEVER; HE ADDED THAT THERE WERE NO CONFLICTS. I ALSO BELIEVE WE SHOULD HAVE CONFIRMED OUR ASSIGNMENT WITH THE FINAL CTLR UPON CHK-ON. USUALLY THEY DO BUT THEY WERE BUSY AND I DID NOT CHK.