The Retest of the High Scorers
Scores on two sittings of an exam have the same distribution in the population, with mean 500, standard deviation 100, and correlation 3/5; assume the relationship is linear. Among students who scored 680 on the second sitting, what is the expected score on the first sitting?
Related problems & prerequisites
Worth solving first
Source: Regression to the mean after Francis Galton. Statement written for AxiomIQ.