According to the Current Population Survey (Internet release date: September 15, 2004), 46% of females between the ages of 18 and 24 years lived at home in 2003. A survey is administered at a community college to 200 randomly selected female students between the ages of 18 and 24 years, and 110 of them respond that they live at home.

(a) Approximate the probability that such a survey will result in at least 110 of the respondents living at home under the assumption that the true percentage is 46%.

(b) Does the result from part (a) contradict the results of the Current Population Survey? Explain.