Question

kaitlyn and allison took a standardized algebra test in different states. kaitlyn takes the test for virginia and scores a 458. allison takes the test for north carolina and scores a 185. suppose the mean and standard deviation for the algebra scores for virginia are 405 and 30, respectively, and the mean and standard deviation for the algebra scores for north carolina are 152 and 20, respectively. which student did better on her algebra test?

kaitlyn and allison did equally well since their scores are both above the mean.
kaitlyn did better since her z-score is higher than allisons z-score.
allison did better since her z-score is higher than kaitlyns z-score.
allison did better since her z-score is closer to the mean than kaitlyns z-score.

Explanation:

Step1: Calculate Kaitlyn's z-score

Use $z = \frac{x - \mu}{\sigma}$. For Kaitlyn: $x=458$, $\mu=405$, $\sigma=30$.
$z = \frac{458 - 405}{30} = \frac{53}{30} \approx 1.77$.

Step2: Calculate Allison's z-score

For Allison: $x=185$, $\mu=152$, $\sigma=20$.
$z = \frac{185 - 152}{20} = \frac{33}{20} = 1.65$.

Step3: Compare z-scores

1.77 (Kaitlyn) > 1.65 (Allison). Higher z-score means better performance.

Answer:

B. Kaitlyn did better since her z-score is higher than Allison's z-score.