Question

Scores on the SAT and ACT are normally distributed. total sat scores (verbal plus math) have a mean of 1011 with a standard deviation of 216. Total ACT scores have a mean of 21 with a standard deviation of 5.3. sofia got 890 on the SAT and 17 on the ACT .she is applying to a college that allows her to report only one test score. Should she report her SAT score or her ACT score? .Do any computations you need here:

Answer 1

Sofia should report her SAT score to the college, as her SAT z-score of -0.56 indicates she performed relatively better on the SAT compared to her ACT z-score of -0.75, considering the respective means and standard deviations of both tests.

Step-by-step explanation:

To decide whether Sofia should report her SAT score or her ACT score to the college, we can calculate the z-scores for each test and compare them. The z-score indicates how many standard deviations an individual score is from the mean.

For the SAT score, the z-score is calculated as follows:

Z_{SAT} = \frac{(Score_{SAT} - Mean_{SAT})}{SD_{SAT}} = \frac{(890 - 1011)}{216} = -0.56

For the ACT score, the z-score is calculated as:

Z_{ACT} = \frac{(Score_{ACT} - Mean_{ACT})}{SD_{ACT}} = \frac{(17 - 21)}{5.3} = -0.75

A higher z-score corresponds to a better performance relative to the mean. Since Sofia's z-score for the SAT is higher (-0.56) than for the ACT (-0.75), she performed relatively better on the SAT in comparison to her peers. Therefore, she should report her SAT score to the college.