Use a normal approximation to find the probability of the indicated number of voters. In this​ case, assume that 141 eligible voters aged​ 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged​ 18-24, 22% of them voted. Probability that fewer than 36 voted

Answer: 0.8770Step-by-step explanation:Given : The number of eligible voters aged​ 18-24 are randomly selected : n=141The population proportion of eligible voters aged​ 18-24 : p=0.22Then, 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]