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 Xwith mean 446 and standard deviation 106. Scores Y of children of parents with graduate degrees have mean 564 and standard deviation 105. 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.) 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 Xwith mean 446 and standard deviation 106. Scores Y of children of parents with graduate degrees have mean 564 and standard deviation 105. 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.)

Explanation / Answer

here for mean of a+bX =500

therefore a+446b =500 .................(1)

also for std deviation of X =100

hence b*106 =100
b=100/106 =0.94

putting it in above : a =79.25

similarly for Y:

c+564d =500 .............(2)

and 105d=100

d=0.95

and c =500-564*0.95 =-37.14

hence a =79.25 ; b=0.94 ; c=-37.14 ; d=0.95

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