How large of a poll (size N) do you need so that P(p^ > 0.5) is at least 99%?

MATLAB: An Introduction with Applications
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Suppose your friend Joanna is running for class president. The proportion of individuals in a population of students who will vote for Joanna on election day is 55%. You plan to conduct a poll of size n and report X, the number of individuals in your poll who plan to vote for Joanna. You also plan to compute p^ = X/n, the proportion of individuals in your poll who plan to vote for Joanna.

f) How large of a poll (size N) do you need so that P(p^ > 0.5) is at least 99%? 

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