A Bias against Trump from Day One?

The post that was quoted here has been removed

I first heard about Marilyn vos Savant in a novel that I read as a child in 2007 about a stereotypically ASD child (peas cannot touch carrots because they are green and carrots are orange, etc - you get the picture). The book is called "The Curious Incident of the Dog in the Night-time", and the main character discusses Marilyn vos Savant and the Monty Hall problem. When I read the book, I was incapable of comprehending the conditional probability behind the problem.

The post that was quoted here has been removed

This is an interesting problem. 2000 is the minimum number of students where more than 1 could be geniuses if the sample were perfectly proportional, but does the fact that 2000 is a sample of the population mean that the random variable in question (the number of people of IQ 145-150 or greater in the sample) follows the hypergeometric distribution? It is possible for there to be more than one person of 145-150 IQ in a school of 1000, so 2000 is really just an arbitrary choice. At what population size could you safely make the assumption that people of IQ higher than 145-150 are in exactly the proportion to the population that is implied by the Gaussian distribution? I suppose that you would have to assume perfect proportionality amongst an arbitrary larger population size to use the probability mass function of a hypergeometrically distributed random variable.

This is, of course, assuming that there is a representative cross-section of society at school X (i.e. it's random), as schools often have academic requirements that skew the mean of intelligence among their pupils. I suppose that one could make some unrealistic/dubious assumptions to be able to calculate probabilities:

If there are 3000 people in the population with 3 geniuses (if, for the sake of brevity, we define "genius" as being IQ of 145-150 or greater), then the probability of there being more than 1 genius in a sample of 2000 is about 74.08%

If the population is 5000 with 5 geniuses, then the probability of there being more than 1 genius in a sample of 2000 is about 66.31%

If the population is 10000 with 10 geniuses, then the probability of there being more than 1 genius in a sample of 2000 is about 62.43%

The probability of drawing more than 1 genius in a sample of 2000 will decrease at a decreasing rate as the population size from which the sample is drawn increases, eventually stabilizing at about 59.41%

Once again, I'm a little bit confused because I'm not sure whether the arbitrarily chosen population size itself must be considered a sample or not.

This problem reminds me a bit of another discussion that you, Wolfgang59 and I were having in mid to late June this year in the thread"Phoenix Police", except that example was more clear-cut because we assumed that the population from which we were drawing contained 10% "bad cops" in every case.

Edit: Here is that discussion: https://www.redhotpawn.com/forum/debates/phoenix-police.181416/page-2

@sonhouse said
@KazetNagorra
Still, if you talk to folks with IQ of 80 and then talk to folks with IQ of 120, you will see an obvious difference which will show up in the first couple of minutes talking to them.

Those are not the tails of the distribution. Neither are they the kind of numbnuts likely to brag about their three little digits.

@shallow-blue said
Those are not the tails of the distribution. Neither are they the kind of numbnuts likely to brag about their three little digits.

Three digits? How generous of you... President Trump likes to brag about his two digits! The Dunning-Kruger effect at work.

@sonhouse said
@KazetNagorra
Still, if you talk to folks with IQ of 80 and then talk to folks with IQ of 120, you will see an obvious difference which will show up in the first couple of minutes talking to them.

Not the point.