In a certain year when she was a high school senior Idonna s

In a certain year, when she was a high school senior, Idonna scored 666 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 507 and standard deviation 124. Jonathan took the ACT and scored 25 on the mathematics portion. ACT math scores for the same year were Normally distributed with mean 21.5 and standard deviation 5.4.

Find the standardized scores (±0.01) for both students. Assuming that both tests measure the same kind of ability, who had the higher score?

Idonna\'s standardized score is

Jonathan\'s standardized score is

Idonna\'s score is higher than Jonathan\'s

Scores are equal

Idonna\'s score is less than Jonathan\'s

Solution

Note that

z = (x-u)/sigma

Thus, for Idonna,

z(Idonna) = (666-507)/124 = 1.28 [ANSWER]

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Meanwhile, for Jonathan,

z(Jonathan) = (25-21.5)/5.4 = 0.65 [ANSWER]

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Thus, relatively, Idonna has the higher score.

OPTION A: Idonna\'s score is higher than Jonathan\'s. [ANSWER, A]