Didn't refuse; that's normal (8)
I believe the answer is:
accepted
'that's normal' is the definition.
(thesaurus)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for accepted that I've seen before include "Receive willingly" , "Established" , "Welcomed" , "Agreed to receive, or approved" , "Said 'yes'" .)