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 $\mu$ minutes and standard deviation $\sigma$.
$\mu = 70$ minutes
$\sigma = 10$ minutes

Question

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 $\mu$ minutes and standard deviation $\sigma$.
$\mu = 70$ minutes
$\sigma = 10$ minutes

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Z-Score Formula" ], "new_concepts": [], "current_concepts": [ "Z-Score Formula", "Normal Distribution" ] } ## Identify the given parameters Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &\mu = 70\ &\sigma = 10 \end{aligned} $$ ## Define the condition for a positive z-score Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z = \frac{x - \mu}{\sigma} > 0 \implies x > \mu\ &x > 70 \end{aligned} $$ ## Evaluate each student's completion time Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &\text{Aaliyah: } x = 55 \implies 55 < 70 \quad (\text{Negative } z)\ &\text{Benjamin: } x = 86 \implies 86 > 70 \quad (\text{Positive } z)\ &\text{Cynthia: } x = 72 \implies 72 > 70 \quad (\text{Positive } z) \end{aligned} $$

Aaliyah, who completed the exam in 55 minutes

Benjamin, who completed the exam in 86 minutes

Cynthia, who completed the exam in 72 minutes

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Z-Score Formula" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Define the condition for a positive z-score

Evaluate each student's completion time

Answer: