This was an actual anecdote from a discussion with a parent of the child in question. The child in question was probably between four and seven years old. They were being assessed by a professional one on one, not in a classroom setting. They were neither showing off nor in possession of the social skills you assume they surely had to have.

I will add that imposter syndrome is common among adults because it's quite hard to figure out where we stand in relation to other people, so smart adults frequently feel they must be "average" because this is "normal" for them. Children are at substantial disadvantage compared to adults.

Do you need to know if it's 145 verse 155?

Possibly. The standard deviation for IQ tests is just 15 points.

More importantly, a test that only goes to 145 cannot distinguish 145 from 180. Both will likely score 145 or close to it.