Question

Asa is running for student council president of a large school. Based on a poll the day before the election, Asa believes that each student will vote for her with probability 0.52, independently of what any other student does. Since she only needs 50% of the vote to win, this means that she would definitely win if every student voted. However, not every student will vote. Approximately how many students need to vote in order for Asa to be 90% certain that she will win the election (that is, 90% certain that she will receive at least 50% of the votes)?

Answer 1

Asa will be elected if p>0.50 and to be 90% confident of her being elected, we require that

P(p>0.50) = 0.90

Now since the population is large, is asymptotically normal

Therefore,

Comparison with Prob (p>0.50) = 0.90, where

Now using the estimated value of P and p both equals to 0.52