Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 156 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 38 voted
The probability that fewer than 38 of 156 eligible voters voted is _______
(Round to four decimal places as needed.)
Solution
$$ \begin{aligned} &\text { given : } n=156, p(\text { eligible voters })=0.22 \\ &n p=156 * 0.22=34.32 \geq 5 \\ &n(1-p)=156 *(1-0.22)=121.68 \geq 5 \end{aligned} $$
\(\therefore\) Binomial random variable is approximately normal
$$ \operatorname{Mean}(\mu)=n p=156 * 0.22=34.32 $$
Standard deviation \((\sigma)=\sqrt{n p(1-p)}=\sqrt{156 * 0.22 *(1-0.22)}=\sqrt{26.7696}\) formula : \(Z=\frac{X-\mu}{\sigma}\)
\(P(\) fewer than 38\() \Rightarrow P(X
Use continuity correction.
$$ \begin{aligned} &P(X<a)=P(X<a-0.5) \\ &\Rightarrow P(X<37.5) \\ &\Rightarrow P\left(\frac{X-\mu}{\sigma}<\frac{37.5-34.32}{\sqrt{26.7696}}\right) \\ &\Rightarrow P(Z<0.61) \end{aligned} $$
Refer to Z-table to find the probability or use the excel formula "=NORM.S.DIST(0.61, TRUE)" to find the probability.
$$ \Rightarrow 0.7306 $$
\(\therefore\) The probability that fewer than 38 of 156 eligible voters voted is \(0.7306\)
Use a normal approximation to find the probability of the indicated number of voters. In this...
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 110 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 27 voted The probability that fewer than 27 of 110 eligible voters voted is Round to four decimal places as needed.)
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 121 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 33 voted The probability that fewer than 33 of 121 eligible voters voted is . (Round to four decimal places as needed.)
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 122 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 29 voted The probability that fewer than 29 of 122 eligible voters voted is (Round to four decimal places as needed.) Hours
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 198 198 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 49 49 voted The probability that fewer than 49 49 of 198 198 eligible voters voted is nothing . (Round to four decimal places as needed.)
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that107 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 28 voted The probability that fewer than 28 of 107 eligible voters voted is_______
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 139 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 exactly 34 voted The probability that exactly 34 of 139 eligible voters voted is (Round to four decimal places as needed.)
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 127 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 exactly 33 voted The probability that exactly 33 of 127 eligible voters voted is (Round to four decimal places as needed.)
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 115 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 exactly 30 voted The probability that exactly 30 of 115 eligible voters voted is...?
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 129 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 exactly 34 voted The probability that exactly 34 of 129 eligible voters voted is
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 182 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 exactly 43 voted.The probability that exactly 43 of 182 eligible voters voted is _______