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 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
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 data value, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Step2: Calculate z - score for Aaliyah
Given $\mu = 70$, $\sigma=10$, and $x = 55$. Then $z=\frac{55 - 70}{10}=\frac{- 15}{10}=-1.5$.
Step3: Calculate z - score for Benjamin
Given $\mu = 70$, $\sigma = 10$, and $x = 86$. Then $z=\frac{86 - 70}{10}=\frac{16}{10}=1.6$.
Step4: Calculate z - score for Cynthia
Given $\mu = 70$, $\sigma = 10$, and $x = 72$. Then $z=\frac{72 - 70}{10}=\frac{2}{10}=0.2$. Since positive z - scores are required, students with positive z - scores are Benjamin and Cynthia.