use the information on the right to determine which students will have positive z - scores.\naaliyah, who…
use the information on the right to determine which students will have positive z - scores.\naaliyah, who completed the exam in 55 minutes\nbenjamin, who completed the exam in 86 minutes\ncynthia, who completed the exam in 72 minutes\nthe time to complete a standardized exam is approximately normally distributed with mean $mu$ minutes and standard deviation $sigma$.\n$mu = 70$ minutes\n$sigma = 10$ minutes
Answer
Explanation:
Step1: Recall z - score formula
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean and $\sigma$ is the standard deviation. A positive z - score occurs when $x>\mu$.
Step2: Compare each student's time with the mean
- For Aaliyah: $x = 55$, $\mu=70$, since $55<70$, $z=\frac{55 - 70}{10}=\frac{- 15}{10}=-1.5<0$.
- For Benjamin: $x = 86$, $\mu = 70$, since $86>70$, $z=\frac{86 - 70}{10}=\frac{16}{10}=1.6>0$.
- For Cynthia: $x = 72$, $\mu = 70$, since $72>70$, $z=\frac{72 - 70}{10}=\frac{2}{10}=0.2>0$.
Answer:
Benjamin, who completed the exam in 86 minutes; Cynthia, who completed the exam in 72 minutes.