Question

TUI US OPPIVALUIT IU DIRTUAL core: 0 of 1 pt 10 of 15 (11 complete) HW Score: 49.6%, 7.44 of 15 pts X 6.6.9-T Question Help e s Use a normal oximation to find the probability of the indicated number of voters. In this case, assume that 166 eligible voters aged 18-21 are randomly selected our Suppose a previous study showed that among eligible voters aged 18-24.22% of the voted Probability that fewer than 43 voted The probably that fewer than 43 of 166 eligible voters vleis Round to four decimal places as needed.) intinue to bok Solutions and Probability e i n er box and wonickCheck Answer Prison Home 9

Answer 1

SOLUTION

$\mathbf{given:}\;\;n=166,\;p=0.22,\;q=1-p=0.78$

np = 166 * 0.22 = 36.52 > 5

$nq=166*0.78=\mathbf{129.48}\geq 5$

Binomial random variable is approximately normal

$Mean\;(\mu)=np=166*0.22=36.52$

$Standard\;deviation\;(\sigma)=\sqrt{npq}=\sqrt{166*0.22*0.78}=\sqrt{28.4856}$

1 - 1 formula :z =

$P(x<43)\Rightarrow P(x<42.5)\;(continuity\;correction)$

$P(x<42.5)=P\left ( \frac{x-\mu}{\sigma}<\frac{42.5-36.52}{\sqrt{28.4856}} \right )$

Refer Standard normal table/Z-table to find the probability.

$\mathbf{{\color{Red} 0.8686}}$