The complete question is:
Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is NOT true?
Options:
A) The ACT score of 17.0 is relatively better than the SAT score of 1490
B) An SAT score of 1490 has a z score of -0.09
C) The SAT score of 1490 is relatively better than ACT score of 17.0
D) An ACT score of 17.0 has a z score of -0.85
To compare scores on different scales or from different groups you need to use a normalized standardized statistic, like the z-score.
[tex]z-score=(score-\mu)/\sigma[/tex]
Where [tex]\mu[/tex] is the mean of the sample, and [tex]\sigma[/tex] is the standard deviation.
1. Find the z-core for an ACT score of 17.0
[tex]z-score=(score-\mu)/\sigma\\ \\ z-score=(17.0-21.1)/4.8\\ \\ z-score=-0.85[/tex]
That means that the ACT score of 17.0 is 0.85 standard deviations below the meqan.
2. Find the z-score for an SAT score of 1490
[tex]z-score=(score-\mu)/\sigma\\ \\ z-score=(1490-1518)/325\\ \\ z-score=-0.086\approx -0.09[/tex]
That means that the SAT score of 1490 is 0.09 standard deviations from the mean.
3. Conlusion:
Since the z-score of the SAT score of 1490 is greater than the z-score of the ACT of 17.0, the SAT score of 1490 is relatively better than the aCT score of 17.0.
As for the answer choices:
