Find the normal approximation for IQ with both genetic and environmental effects. What is the maximum possible IQ with the model?
Suppose that scientists develop a new model of human IQ that includes three independent factors: genes of large effect, genes of small effect, and environmental effects. All genes are assumed to be dominant. There are ten smart genes of large effect, each of which adds 2.5 IQ points. There are 20 smart genes of small effect, each of which adds 0.6 IQ points. There are 30 environmental factors, with favorable ones adding 0.9 IQ points. People have a baseline IQ of 80 if they have no favorable effects. Finally, suppose that the probability of getting each smart gene is 0.75, and the probability of getting each favorable environmental effect is 0.5.