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: $mu = 41.0$, $sigma = 9.4$. best supporting actor: $mu = 51.0$, $sigma = 14$. in a particular year, the best actor was 39 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.)

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, $x = 39$, $\mu=41.0$, and $\sigma = 9.4$. Substitute these values into the z - score formula:
$z_{1}=\frac{39 - 41.0}{9.4}=\frac{- 2}{9.4}\approx - 0.21$

Step3: Calculate z - score for Best Supporting Actor

For the Best Supporting Actor, $x = 83$, $\mu = 51.0$, and $\sigma=14$. Substitute these values into the z - score formula:
$z_{2}=\frac{83 - 51.0}{14}=\frac{32}{14}\approx2.29$

Answer:

Best Actor: $z\approx - 0.21$
Best Supporting Actor: $z\approx2.29$