Question 1009995: Can someone please help?
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 185 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 46 voted
The probability that fewer than 46 of 185 eligible voters voted is _____.
(Round to four decimal places as needed.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 185 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
mean = np = 0.22*185 = 40.7
std = sqrt(npq) = sqrt(185*0.22*0.78) = 5.634
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Probability that fewer than 46 voted
Binomial need:: P(x < 46)
Normal approx need:: P(x < 46.5)
P(46.5) = P(z < z(
z(46.5) = (46.5-40.7)/5.634 = 5.8/5.634 = 1.0295
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P(x < 46.5) = P(z < 1.0295) = 0.8484
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The probability that fewer than 46 of 185 eligible voters voted is 0.8484.
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Cheers,
Stan H.
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