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Hmm, is it still binomial if each individual question has different p of being correct? Also you will have to shift and rescale the binomial distribution to get
by rawnlq 11y ago
Hmm, is it still binomial if each individual question has different p of being correct? Also you will have to shift and rescale the binomial distribution to get it to have a mean of 100 and a std dev of 15 (which iq is defined as).
But you did answer my question on why IQ is normally distributed: the IIDs being averaged are the test questions themselves! (although I don't fully understand if those questions are bernoullis?)
- rawnlq 11y agoThinking about it more I think it makes more sense to have N as the number of test takers. That way you can model it as a question x having a probability p_x of being correct. Then the total grade on problem x will be a binomial(N, p_x), which will converge to a normal distribution for large number of test takers. Then you are simply summing up a small number of normal approximations to get the final grade (and sum of normals is normal). Did I model that correctly?