The College Board finds that the distribution of students\' SAT scores depends o

Question

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 444 and standard deviation 101. Scores Y of children of parents with graduate degrees have mean 555 and standard deviation 102. Perhaps we should standardize to a common scale for equity. Find numbers a, b, c, and d such that a + bX and c + dY both have mean 500 and standard deviation 100. (Round your answers to two decimal places.) a = b = c = d =

Explanation / Answer

To standardize mean 444, standard deviation 100:

b = 100/101
   b =0.9900

Then, a+bX
100/101 * 444 + a = 500
a = 500 - 100/101 * 444
a = 60.44

mean 555 and standard deviation 102
d = 100/102
   d =0.9803

c = 500 - 100/102 * 555
c= -43.9
Therefore
a= 60.44
b =0.9900
c= -43.9
d =0.9803

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