To paraphrase a psychiatrist friend of my wife:
"Most of the time in psychology, normal simply means very much alike everyone else around you. It's quantative, not qualitative."
Hence no scare-quotes.
To add to your sub-thread on intelligence/IQ: normal IQ here for swedes is 100. That means someone with 65 or 135 is less normal, and someone with an extreme value like 165 is abnormal.
I mention this because since a single IQ is relative all other test-scores and is only meaningful in relation to all the other scores; on its own it doesn't say much at all. A person with 150+ is so rare, they have trouble communicating and understanding those with normal intelligence.
Then again, IQ is a very blunt measurement, sort of a yard-stick with only feet, no inches.
Eh, it's bedtime for me - good night!