rainforest data: mean = 7, $\sigma^2 = 12.405$, $\sigma \approx 3.522$ when using the formula $z_x = \frac{x - \mu}{\sigma}$ for the z-score for the 11.7 data point: $x = 11.7$, $\mu = 7$ $z_{11.7} \approx 1.3$ is 11.7 within a z-score of 3? - yes because $z_{11.7} 3$

Question

rainforest data:

mean = 7, $\sigma^2 = 12.405$, $\sigma \approx 3.522$

when using the formula $z_x = \frac{x - \mu}{\sigma}$ for the z-score for the 11.7 data point:

$x = 11.7$, $\mu = 7$

$z_{11.7} \approx 1.3$

is 11.7 within a z-score of 3?

- yes because $z_{11.7} < 3$
- yes because $z_{11.7} = 3$
- no because $z_{11.7} > 3$

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", "Population Mean Symbol" ], "new_concepts": [], "current_concepts": [ "Z-Score Formula", "Population Mean Symbol", "Population Standard Deviation" ] } ## Identify given values and formula Using the *Population Mean Symbol* and *Z-Score Formula* knowledge points $$ \begin{aligned} &x = 11.7\ &\mu = 7\ &\sigma \approx 3.522\ &z_x = \frac{x - \mu}{\sigma} \end{aligned} $$ ## Calculate the z-score Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z_{11.7} = \frac{11.7 - 7}{3.522}\ &z_{11.7} = \frac{4.7}{3.522} \approx 1.33 \end{aligned} $$ ## Compare the z-score to the threshold Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z_{11.7} \approx 1.33 < 3 \end{aligned} $$

Yes because $z_{11.7} < 3$

Yes because $z_{11.7} = 3$

No because $z_{11.7} > 3$

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

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QUESTION IMAGE

Question

Explanation:

Identify given values and formula

Calculate the z-score

Compare the z-score to the threshold

Answer: