Question

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.

Answer 1

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  = (x_1-1)/ ₁

= (1220 - 1000)/75)

= 220/75

= 2.933

the z value of the test B score is Z  = (x_2-2)/ ₂

= (39 - 27)/4

= 12/4

= 3

The test B has higher relative score then test A