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: $mu = 46.0$, $sigma = 7.8$; best supporting actor: $mu = 51.0$, $sigma = 14$. in a particular year, the best actor was 45 years old and the best supporting actor was 65 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

For the Best Actor, $\mu = 46.0$, $\sigma=7.8$, and $x = 45$.
$z_{1}=\frac{45 - 46.0}{7.8}=\frac{-1.0}{7.8}\approx - 0.13$

Step3: Calculate z - score for Best Supporting Actor

For the Best Supporting Actor, $\mu = 51.0$, $\sigma = 14$, and $x = 65$.
$z_{2}=\frac{65 - 51.0}{14}=\frac{14}{14}=1.00$

Answer:

Best Actor: $z\approx - 0.13$
Best Supporting Actor: $z = 1.00$