use the information on the right to determine which students will have positive z - scores. aaliyah, who…
use the information on the right to determine which students will have positive z - scores. aaliyah, who completed the exam in 55 minutes benjamin, who completed the exam in 86 minutes cynthia, who completed the exam in 72 minutes done the time to complete a standardized exam is approximately normally distributed with mean μ minutes and standard deviation σ. μ = 70 minutes σ = 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 $55<70$, $z=\frac{55 - 70}{10}=\frac{- 15}{10}=-1.5$ (negative z - score). For Benjamin: $x = 86$, $\mu = 70$, since $86>70$, $z=\frac{86 - 70}{10}=\frac{16}{10}=1.6$ (positive z - score). For Cynthia: $x = 72$, $\mu = 70$, since $72>70$, $z=\frac{72 - 70}{10}=\frac{2}{10}=0.2$ (positive z - score).
Answer:
Benjamin, Cynthia