Question

In a recent awards​ ceremony, the age of the winner for best actor was 35 and the age of the winner for best actress was 54. For all best​ actors, the mean age is 42.1 years and the standard deviation is 6.6 years. For all best​ actresses, the mean age is 34.3 years and the standard deviation is 10.1 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.

Answer 1

Answer:

The actress has the more extreme age because

Step-by-step explanation:

Given

Male Athletes:

$x = 35$

$\=x = 42.1$

$SD = 6.6$

Female Athletes

$x = 54$

$\=x = 34.3$

$SD = 10.1$

Required

Determine which athlete had more extreme age

To do this, we simply calculate the standard z score using

$z = \frac{x - \=x}{SD}$

For the actor:

$z = \frac{35 - 42.1}{6.6}$

$z = \frac{-7.1}{6.6}$

$z = 1.0758$

For the actress:

$z = \frac{54 - 34.3}{10.1}$

$z = \frac{19.7}{10.1}$

$z = 1.950$

Comparing both z values;

The actress has the more extreme age because

• It has a positive z value
• Its z value is greater than that of the actor