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: $z = -0.40$
best supporting actor: $z = 2.27$
(round to two decimal places as needed.)

interpret the z-scores.
the best actor was dropdown the mean, which dropdown unusual. the best supporting actor was dropdown the mean, which dropdown unusual.

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: $z = -0.40$
best supporting actor: $z = 2.27$
(round to two decimal places as needed.)

interpret the z-scores.
the best actor was dropdown the mean, which dropdown unusual. the best supporting actor was dropdown the mean, which dropdown unusual.

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", "Z-Score Interpretation" ], "new_concepts": [], "current_concepts": [ "Z-Score Calculation", "Z-Score Interpretation" ] } ## Calculate the z-scores Using the *Z-Score Calculation* knowledge point $$ \begin{aligned} z_{\text{Actor}} &= \frac{x - \mu}{\sigma} = \frac{42 - 45.0}{7.5} = -0.40 \ z_{\text{Supporting}} &= \frac{x - \mu}{\sigma} = \frac{83 - 49.0}{15} \approx 2.27 \end{aligned} $$ ## Interpret the Best Actor z-score Using the *Z-Score Interpretation* knowledge point $$ \begin{aligned} &z_{\text{Actor}} = -0.40 \ &\text{Since } -1 < z < 0\text{, the age is less than 1 standard deviation below the mean.} \ &\text{Since } |z| \le 2\text{, this value is not unusual.} \end{aligned} $$ ## Interpret the Best Supporting Actor z-score Using the *Z-Score Interpretation* knowledge point $$ \begin{aligned} &z_{\text{Supporting}} = 2.27 \ &\text{Since } 2 < z < 3\text{, the age is more than 2 standard deviations above the mean.} \ &\text{Since } |z| > 2\text{, this value is unusual.} \end{aligned} $$ The Best Actor was less than 1 standard deviation below the mean, which is not unusual. The Best Supporting Actor was more than 2 standard deviations above the mean, which is unusual. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Z-Score Interpretation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the z-scores

Interpret the Best Actor z-score

Interpret the Best Supporting Actor z-score

Answer: