Question

The distribution of ages of Oscar winning actresses is roughly symmetric and mound shaped (in other words, the ages for Oscar winning actresses are normally distributed). The mean of this distribution is 36 years and the standard deviation of this distribution is 11 years.In 2013, Jennifer Lawrence and Daniel Day-Lewis won the Oscar for best leading actress and best leading actor respectively. Jennifer Lawrence was 22 years old and Daniel Day-Lewis was 55 years old

a.Which is more unusual – an actress who receives an Oscar at 22 or an actor

receives an Oscar at 55?

b.Which is more unusual – an actress who receives an Oscar at 55 or an actor who receives an Oscar at 55? Calculate the standard score for the 55 year old actress. Calculate the standard score for the 55 year old actor. Then answer the question and explain your answer.

c.It is more unusual for Daniel Day-Lewis to receive the Oscar at age 55 because a large percentage of actors receive Oscars at age 55 or older

d. It is more unusual for Jennifer Lawrence to receive an Oscar at age 22 because a small percentage of actresses receive Oscars at age 22 or younger

Answer 1

X be the ages of Oscar winning actresses and it follows normal distribution with mean µ = 36 and standard deviation σ = 11

Y be the ages of Oscar winning actors and it follows normal distribution with mean µ = 44 and standard deviation σ = 9

#a) z score for age x = 22

z =  

z = -1.27

z score for y = 55

z =

z = 1.22

z = -1.27 is more away from 0 than z = 1.22 , therefore an actress who receives an Oscar at 22 is more unusual.

#b) z score for x = 55

z =  

z = 1.73

We have z score for y = 55 is 1.22

As z =1.73 is more away from 0 than z = 1.22 , therefore an actress who receives an Oscar at 55 is more unusual.

#c) P( x > 55 )

= P( z > 1.73 )

= 1 - P( z <1.73 )

= 1 - 0.9582

= 0.0418 ~ 4.18%

4.18% is less than 5% therefore .Yes, It is more unusual for Daniel Day-Lewis to receive the Oscar at age 55

#d) P ( x < 22 )

= P ( z < -1.27 )

= 0.1020 ~ 10.20%

10.20% is more than 5% therefore It is not unusual for Jennifer Lawrence to receive an Oscar at age 22