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. compute the z - scores for the actors in the following situation.
best actor: $mu = 46.0$, $sigma = 8.8$
best supporting actor: $mu = 49.0$, $sigma = 10$
in a particular year, the best actor was 54 years old and the best supporting actor was 45 years old.
determine the z - scores for each.
best actor: $z=square$
best supporting actor: $z = square$
(round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for Best Actor

Given $\mu_{BA}=46.0$, $\sigma_{BA}=8.8$, and $x_{BA}=54$.
$z_{BA}=\frac{54 - 46.0}{8.8}=\frac{8}{8.8}\approx0.91$

Step3: Calculate z - score for Best Supporting Actor

Given $\mu_{BSA}=49.0$, $\sigma_{BSA}=10$, and $x_{BSA}=45$.
$z_{BSA}=\frac{45 - 49.0}{10}=\frac{- 4}{10}=-0.40$

Answer:

Best Actor: $0.91$
Best Supporting Actor: $-0.40$