What's the Probability of Two People Having an IQ of 142 (15sd) or Higher in a Sample Size of 380 People?

Question

A boy in my school year claims an IQ score, on a 15sd test, of 142. Having researched this, I found that the rarity of this score (or higher) is 1 person in 391 for that age (15 years). There are 380 people in my year, so what is the probability of another person (a total of two people) having this IQ or greater in the year? And what about 3 people? 4 people?... I know there are a lot of intelligent people out there, probably with their own high IQs, so please help me!

Answer 1

I've got about the same, not sure the exact #.  As for how many other people could have around the same intelligence or around 1 pt lower there using the rarity charts out there 1/ 391=142 1/319=141 so there could be 72 other people in your class with IQs between 141-142.  I'm pretty sure that theoretically there shouldn't be too many people in your class with a higher IQ than this, maybe someone with a few pts but nothing more than that.  But this is all based on a perfectly random sample of individuals, and the real world isn't always modeled like that. Also there's some evidence that the normal curve isn't the most accurate to model IQ scores, but I don't remember what the other distribution I read about was.  As for a more mathy answer I'm pretty sure this can be modeled with the following formula. I'm going to fudge it and say that 1/380 aprox =1/391.  so the prob in your school of having a 142 or higher is 1/380=.0026=.26 % (that's a quarter of a percent)   So maybe (and I could be wrong here), the prob of one is .26%, the prob of two is .26%*.26 %=.000676% and the prob of three would be .26%^3....and so on.