Suppose that a particular candidate for public office is in

Suppose that a particular candidate for public office is in fact favored by 47% of all registered voters in the district. A polling organization will take a random sample of 550 voters and will use p?, the sample proportion, to estimate p. What is the approximate probability that p? will be greater than .5, causing the polling organization to incorrectly predict the result of the upcoming election? (Round your answer to four decimal places.)

Solution

The probability is

P(phat>0.5) = P((phat-p)/sqrt(p*(1-p)/n) >(0.5-0.47)/sqrt(0.47*(1-0.47)/550))

=P(Z>1.41) =0.0793 (from standard normal table)