Question: The College board finds that child SAT scores are associated with parent education level. For parents not finishing high school, child SAT scores X have mean 442 and standard deviation 108. For parents with graduate degrees, child SAT scores Y have mean 566 and standard deviation 109. To make valid comparisons between X and Y scores, we must first convert them to a common measuring scale. Find four exact numbers a, b, c, and d in reduced fraction form, such that (a + bX) and (c + dY) both have mean 500 and standard deviation 100.