Just before a city referendum on a school budget, a local newspaper polls 430 vo

Question

Just before a city referendum on a school budget, a local newspaper polls 430 voters in an attempt to predict whether the budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 51% of the voters.

Question: What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, that is, what is the probability that the newspaper's sample results in a sample proportion less than 0.50 in favor of the referendum?

?????(calculate the standard deviation of to 4 decimal places, round your final answer to 4 decimal places).

Explanation / Answer

The probability is
P(phat<0.5)
=P((phat-p)/[p*(1-p)/n] <(0.5-0.54)/sqrt(0.54*(1-0.54)/430))

=P(Z<-1.66)

=0.0485 (check standard normal table)

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