In 2013, when she was a high school senior, Idonna scored 670 on the mathematics part of the SAT. 5 The distribution of SAT math scores in 2013 was Normal with mean 514 and standard deviation 118. Jonathan took the ACT and scored 26 on the mathematics portion. ACT math scores for 2013 were Normally distributed with mean 20.9 and standard deviation 5.3.

A: Find the standardized scores for both students.

B. Assuming that both tests measure the same kind of ability, Who had the higher score?

Question

Devyn Villanueva

Mathematics

28 October, 21:22

In 2013, when she was a high school senior, Idonna scored 670 on the mathematics part of the SAT. 5 The distribution of SAT math scores in 2013 was Normal with mean 514 and standard deviation 118. Jonathan took the ACT and scored 26 on the mathematics portion. ACT math scores for 2013 were Normally distributed with mean 20.9 and standard deviation 5.3.

A: Find the standardized scores for both students.

B. Assuming that both tests measure the same kind of ability, Who had the higher score?

+2

Answers (1)

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Huber · Answer 1

The standardized z-score is calculated as (actual score - mean) / (standard deviation).

A. Idonna's z-score would be (670 - 514) / 118 = 1.322

Jonathan's z-score would be (26 - 20.9) / 5.3 = 0.962

B. This implies that Idonna's score is higher, since it is more standard deviations above the mean.