Question

In a recent awards​ ceremony, the age of the winner for best actor was 32 and the age of the winner for best actress was 50. For all best​ actors, the mean age is 41.3 years and the standard deviation is 5.4 years. For all best​ actresses, the mean age is 35.3 years and the standard deviation is 10.2 years.​ (All ages are determined at the time of the awards​ ceremony.) Relative to their​ genders, who had the more extreme age when winning the​ award, the actor or the​ actress? Explain.

Since the z score for the actor is z=? and the z score for the actress is z=?​, the actress/actor had the more extreme age.

Answer 1

$\bar x_{actor}=41.3$

$s_{actor}=5.4$

$x_{actor}=32$

$\bar x_{actress}=35.3$

$s_{actress}=10.2$

$x_{actress}=50$

$$Z=\frac{x-\bar x}{s}$$

So

$Z_{actor}=\frac{32-41.3}{5.4}=-1.72$

$Z_{actress}=\frac{50-35.3}{10.2}=1.44$

Since the value of $Z_{actor}$ is higher than the value of $Z_{actress}$ (absolute value), thus the value of $x_{actor}$ is further from the mean compare to the value of $x_{actress}$. Therefore the actor has more extreme age.