Question
In: Math
Two standardized tests, test A and test B, use very different scales. Assume that in one...
Two standardized tests, test A and test B, use very different scales. Assume that in one year the distribution of scores on test A can be modeled by N(1000, 75) and scores on test B can be modeled by N(27, 4). If an applicant to a university has taken test A and scored 1220 and another student has taken test B and scored 39, compare these students' scores using z-values. Which one has a higher relative score? Explain.
Solutions
Expert Solution
Answer :
given data :-
student has taken test A and scored = 1220
X1 = 1220
student has taken test B and scored = 39
X2 = 39
distribution of scores on test A can be modeled by = 1000
1 =
1000
distribution of scores on test B can be modeled by = 27
2 =
27
standard deviation = 75
1 =
75
standard deviation = 4
2 =
4
now we need to find out a higher relative score
we know that
z = (x- )/
the z value of the test A score is Z =
(x1-1)/
1
= (1220 - 1000)/75)
= 220/75
= 2.933
the z value of the test B score is Z =
(x2-2)/
2
= (39 - 27)/4
= 12/4
= 3
The test B
has higher relative score then test A
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