91Ó°ÊÓ

Congressional candidate \(\mathrm{X}\) will base his decision on whether or not to endorse the Educational Opportunity Act on the results of a poll of a random sample of 200 registered voters from his district. He will endorse the Educational Opportunity Act only if 100 or more voters are in favor if it. (a) What is the probability that candidate \(\mathrm{X}\) will endorse the Act if \(45 \%\) of all registered voters in his district are in favor of it? (b) What is the probability that candidate \(\mathrm{X}\) will fail to endorse the Act if \(52 \%\) of all voters in his district are in favor of it?

Show by integrating, that \(\mathrm{f}(\mathrm{x})=\left[1 /\left\\{\sigma \sqrt{(2 \pi)\\}]} \exp \left[-(1 / 2)\\{(\mathrm{X}-\mu) / \sigma\\}^{2}\right]\right.\right.\) the normal distribution, is an actual probability density function.