The College Board finds that the distribution of students\' SAT scores depends o
ID: 3327567 • Letter: T
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 451 and standard deviation 107. Scores Y of children of parents with graduate degrees have mean 565 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.)
a=
b=
c=
d=
Explanation / Answer
We first find Z value for each of the random variables, and then express that Z with new distribution which has the comon mean and deviation of 500 and 100.
a.Children of parents who did not finish high school have SAT math scores X with mean 451 and standard deviation 107.
Z = (X-451)/107
And with new mean and deviation = >
a. 500 + (100)*(X-451)/107
500 + (100/107)*X - 100*451/107
= 78.5 + .9345X
a = 78.51, b = .94
b.
And with new mean and deviation = >
b. 500 + (100)*(X-565)/105
500 + (100/105)*X - 100*465/105
= 57.14 + .952X
c = 57.14, d = .95
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