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 454 and standard deviation 102. Scores Y of children of parents with graduate degrees have mean 563 and standard deviation 104. 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

for mean of a+bX = a+bE(X)=500

a+454b=500 ............(1)

and mean of c+dY =c+dE(Y)=500

c+563d=500.........(2)

also std deviation of a+bX =b*SD(X)=100

b*102= 100

b=100/102=0.9804

putting it in equation (1)

a=454*(100/102)=50

a=54.902

similarly std deviaiton of c+dY =d*SD(Y)=100

d*104=100

d=100/104 =0.9615

putting it in equation 2

c+563*(100/104)=500

c=-41.3462

hence a =54.902 ; b=0.9804 ; c=-41.3462 ; d=0.9615

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.