Question

In a recent awards​ ceremony, the age of the winner for best actor was

29

and the age of the winner for best actress was

50.

For all best​ actors, the mean age is

43.9

years and the standard deviation is

8.7

years. For all best​ actresses, the mean age is

37.5

years and the standard deviation is

12.2

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.

Answer 1

Solution :

Given that ,

mean = = 43.9 ( actors)

standard deviation =  = 8.7

x = 29

Using z-score formula,

z = x - /   

z = 29 - 43.9 / 8.7

z = -1.71 ( actors)

mean = = 37.5 ( actresses)

standard deviation =  = 12.2

x = 50

Using z-score formula,

z = x - /   

z = 50 - 37.5 / 12.2

z = 1.02 ( actresses)

Since the z-score for the actor is z = -1.71 and the z-score for the actresses is z = 1.02, the actresses had the more extreme age