During her senior year, Courtney took both the SAT and ACT. She scored 680 on the SAT math test and 27 on the ACT math test. Scores on the math section of the SAT vary from 200 to 800, with a mean of 528 and standard deviation of 117. Scores on the math section of the ACT vary from 1 to 36, with a mean of 20.5 and a standard deviation of 5.5.
Calculate Courtney's standardized score (z-score) on each test. Which of her two test scores was better, relatively speaking? Explain your reasoning.

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joaobezerra joaobezerra · Answer 1 · 2022-09-20T11:48:50-04:00

Her z-scores are given as follows:

Due to the higher z-score, she was relatively better on the SAT.

The z-score of a measure X of a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For the SAT test, the parameters are given as follows:

[tex]X = 680, \mu = 528, \sigma = 117[/tex]

Hence her z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (680 - 528)/117

Z = 1.30.

For the ACT test, the parameters are given as follows:

[tex]X = 27, \mu = 20.5, \sigma = 5.5[/tex]

Hence her z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (27 - 20.5)/5.5

Z = 1.18.

Due to the higher z-score, she was relatively better on the SAT.

More can be learned about z-scores at https://brainly.com/question/25638875

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