Answer: 0.8770
Step-by-step explanation:
Given : The number of eligible voters aged 18-24 are randomly selected : n=141
The population proportion of eligible voters aged 18-24 : p=0.22
Then, mean : [tex]np=141(0.22)=31.02[/tex]
Standard deviation: [tex]\sqrt{np(1-p)}=\sqrt{141(0.22)(1-0.22)}\approx4.92[/tex]
We assume that this is normal distribution.
Let X be a binomial variable.
For x =36
[tex]z=\dfrac{x-\mu}{\sigma}\\\\ z=\dfrac{36-31.02}{4.29}\approx1.16[/tex]
The probability that fewer than 36 voted will be :-
[tex]P(x<36)=P(z<1.16)=0.8769756\approx0.8770[/tex]
