Question

In a certain year, when she was a high school senior, Idonna scored 620 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 510 and standard deviation 112. Jonathan took the ACT and scored 29 on the mathematics portion. ACT math scores for that year were Normally distributed with mean 20.4 and standard deviation 5.2.

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 _____

Answer 1

Idonna's standardized score is
`z_1 = 0.98`

Jonathan's standardized score is
`z_2 = 1.65`

Jonathan had the high score

Explanation:

From the question we are told that

The score of Idonna is
`x_1 = 620`

The mean of SAT is
`\mu_1 = 510`

The standard deviation of SAT is
`\sigma_1 = 112`

The score of Jonathan is
`x_2 = 29`

The mean of ACT is
`\mu_2 = 20.4`

The standard deviation of ACT is
`\sigma_2 = 5.2`

The standardized score for Idonna is

`z_1 = (x_1 - \mu_1)/(\sigma_1)`

=>
`z_1 = (620 - 510)/(112)`

=>
`z_1 = 0.98`

The standardized score for Jonathan is

`z_2 = (x_2 - \mu_2)/(\sigma_2)`

=>
`z_2 = (29 - 20.4)/(5.2)`

=>
`z_2 = 1.65`