SOLUTION: In a recent election, 10,000 people voted, 4900 voted for Jones, 5100 voted for Smith. There was a challenge and 1,000 votes were thrown out. Assume p=P(votes for Jones)=4900/10000

Question 61244: In a recent election, 10,000 people voted, 4900 voted for Jones, 5100 voted for Smith. There was a challenge and 1,000 votes were thrown out. Assume p=P(votes for Jones)=4900/10000=.49, and that n=1000. If we randomly throw out 1000 votes, jones will need at least 4501 of the remaining 9000 to win. this means that of the 1000 thrown out, less than 400 must be "Jones" votes in order for him to win.
Q: What is the probability that Jones will win under these conditions? It has to be done with the normal distribution, and I have no idea what that is...help please...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a recent election, 10,000 people voted, 4900 voted for Jones, 5100 voted for Smith. There was a challenge and 1,000 votes were thrown out. Assume p=P(votes for Jones)=4900/10000=.49, and that n=1000. If we randomly throw out 1000 votes, jones will need at least 4501 of the remaining 9000 to win. this means that of the 1000 thrown out, less than 400 must be "Jones" votes in order for him to win.
Q: What is the probability that Jones will win under these conditions? It has to be done with the normal distribution,
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It is a binomial problem with n=1000, p=0.49
Because of the large n you use a Normal Approximation for to find the
probability.
You want P(0<=X<=399)=P((0-(1000)(0.49))/sqrt(1000(0.49)(0.51) <= z
<=((399-490)/sqrt(490*0.51))=0.0000000045407...
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Cheers,
Stan H.
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