Question

There is a 42% chance a 22-26 year old still lives at home

a) Find the probability from a sample of 48 22-26 year olds more than 22 live at home?

b) On average from a sample of 160 22-26 year olds how many do NOT live at home?

Answer 1

P(22-26 year old still lives at home) =p=0.42

a)

let X is number of 22-26 year old who still lives at home out of 48 samples

hence X~Bin(48,0.42)

so

E(X)=n*p=48*0.42=20.16

Var(X)=n*p*(1-p)=48*0.42*0.58=11.6928

we have to find P(X>22)

now

b)

Here n=160

P(22-26 year old who do not still live at home)=q=1-p=1-0.42=0.58

so required value

Expectation=n*q=160*0.58=92.8~93