The Stanford Binet test (the major IQ test that is professionally administered) gives you a score where they match your "mental age" vs. your "real age". It is usually considered to be most accurate when you take it at age 8ish.
So if you take it at age 8, and you score what the "average" 12 year old gets. Then your IQ is 150. (12/8 * 100). there is nothing inherent in this scoring system that will make the distribution normal. Scores are based on nominal performance. Not adjusted.
For instance, if half of 12 year olds think like the average 9 year old, and half thinks like the average 15 year old, then half IQ's would be 75, half would be 125, for an average of 100 within that population for a barbell type distribution. Also, it is entirely possible that 12 year olds are normally distributed, 11 year olds are right tailed, and 13 year olds are left tailed, 15 year olds have kurtosis. But overall together, they are normally distributed for the overall population which is what the Stanford Binet results indicates.