use the information on the right to determine which students will have positive z - scores. aaliyah, who…

Answer:

• Benjamin, who completed the exam in 86 minutes
• Cynthia, who completed the exam in 72 minutes

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the mean and $\sigma$ is the standard deviation.

Step2: Calculate z - score for Aaliyah

For Aaliyah, $x = 55$, $\mu=70$, $\sigma = 10$. Then $z=\frac{55 - 70}{10}=\frac{- 15}{10}=-1.5$.

Step3: Calculate z - score for Benjamin

For Benjamin, $x = 86$, $\mu=70$, $\sigma = 10$. Then $z=\frac{86 - 70}{10}=\frac{16}{10}=1.6$.

Step4: Calculate z - score for Cynthia

For Cynthia, $x = 72$, $\mu=70$, $\sigma = 10$. Then $z=\frac{72 - 70}{10}=\frac{2}{10}=0.2$.

Step5: Determine positive z - scores

Since $z_{Benjamin}=1.6>0$ and $z_{Cynthia}=0.2>0$, while $z_{Aaliyah}=-1.5<0$, Benjamin and Cynthia have positive z - scores.