Question

the table shows population statistics for the ages of best actor and best supporting actor winners at the academy awards from 1929 to 2020. the distributions of the ages are approximately bell - shaped. compare the z - scores for the actors.

best actor	best supporting actor
$\sigma \approx 8.7$ yr	$\sigma \approx 13.5$ yr

best actor 1930: george arliss, age: 62
best supporting actor 1942: donald crisp, age: 59

determine the z - scores for each.

george arliss: $z \approx \square$
donald crisp: $z \approx \square$
(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 value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for George Arliss

For George Arliss (Best Actor), $x = 62$, $\mu=43.8$, and $\sigma = 8.7$.
Substitute into the formula: $z=\frac{62 - 43.8}{8.7}=\frac{18.2}{8.7}\approx2.09$

Step3: Calculate z - score for Donald Crisp

For Donald Crisp (Best Supporting Actor), $x = 59$, $\mu = 50.2$, and $\sigma=13.5$.
Substitute into the formula: $z=\frac{59 - 50.2}{13.5}=\frac{8.8}{13.5}\approx0.65$

Answer:

George Arliss: $z\approx\boldsymbol{2.09}$
Donald Crisp: $z\approx\boldsymbol{0.65}$