SAT scores. The College Board finds that the distribution of students’ SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT Math...

SAT scores. The College Board finds that the distribution of students’ SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT Math scores X with mean 445 and standard deviation 106. Scores Y of children of parents with graduate degrees have mean 566 and standard deviation 109. Perhaps we should standardize to a common scale for equity. Find positive numbers a, b, c, and d such that a + bX and c + dY both have mean 500 and standard deviation 100.