Question

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 563 and standard deviation 111. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 22.7 and standard deviation 2.1. a. What is Elanor's standardized score? Round to 2 decimal places. b. What is Gerald's standardized score? Round to 2 decimal places. c. Assuming that both tests measure the same kind of ability, who has the higher score? Gerald. Elanor. They both did equally well. Submit Question

Answer 1

a) The z score for Elanor is computed here as:

X-HO Zelanor 680 – 563 111 = 1.0541

Therefore 1.05 is the standardized score here.

b) The z score for Gerald here is computed as:

$z_{Gerald} = \frac{\bar X - \mu_0}{\sigma} = \frac{27 - 22.7}{2.1} = 2.05$

Therefore 2.05 is the required standardized score here.

c) As the z score for Gerald is higher here. Therefore Gerald has a higher score here.