the table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation.

best actor
$\mu = 45.0$
$\sigma = 7.5$

best supporting actor
$\mu = 49.0$
$\sigma = 15$

in a particular year, the best actor was 42 years old and the best supporting actor was 83 years old.

determine the z-scores for each.

best actor: $z = $
best supporting actor: $z = $
(round to two decimal places as needed.)

Question

the table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation.

best actor
$\mu = 45.0$
$\sigma = 7.5$

best supporting actor
$\mu = 49.0$
$\sigma = 15$

in a particular year, the best actor was 42 years old and the best supporting actor was 83 years old.

determine the z-scores for each.

best actor: $z = $
best supporting actor: $z = $
(round to two decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Z-Score Calculation" ], "new_concepts": [], "current_concepts": [ "Z-Score Calculation", "Z-Score Interpretation" ] } ## Identify parameters for Best Actor Using the *Z-Score Calculation* knowledge point $$ \begin{aligned} x_{\text{actor}} &= 42 \ \mu_{\text{actor}} &= 45.0 \ \sigma_{\text{actor}} &= 7.5 \end{aligned} $$ ## Calculate Best Actor z-score Using the *Z-Score Calculation* knowledge point $$ \begin{aligned} z_{\text{actor}} &= \frac{x_{\text{actor}} - \mu_{\text{actor}}}{\sigma_{\text{actor}}} \ z_{\text{actor}} &= \frac{42 - 45.0}{7.5} \ z_{\text{actor}} &= \frac{-3}{7.5} = -0.40 \end{aligned} $$ ## Identify parameters for Best Supporting Actor Using the *Z-Score Calculation* knowledge point $$ \begin{aligned} x_{\text{supporting}} &= 83 \ \mu_{\text{supporting}} &= 49.0 \ \sigma_{\text{supporting}} &= 15 \end{aligned} $$ ## Calculate Best Supporting Actor z-score Using the *Z-Score Calculation* knowledge point $$ \begin{aligned} z_{\text{supporting}} &= \frac{x_{\text{supporting}} - \mu_{\text{supporting}}}{\sigma_{\text{supporting}}} \ z_{\text{supporting}} &= \frac{83 - 49.0}{15} \ z_{\text{supporting}} &= \frac{34}{15} \approx 2.2667 \approx 2.27 \end{aligned} $$ Determine the z-scores for each. Best Actor: $z =$ -0.40 Best Supporting Actor: $z =$ 2.27 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Z-Score Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify parameters for Best Actor

Calculate Best Actor z-score

Identify parameters for Best Supporting Actor

Calculate Best Supporting Actor z-score

Answer: