Gun safety. An October 2004 Gallup Poll asked a sample of 1012 adults whether they thought that having a gun in the house makes it a safer place to be or a more dangerous place to be. The number who thought having a gun in the house makes it a safer place was 425. Although the samples in national polls are not SRSs, they are similar enough that our method gives approximately correct confidence intervals.

(a) Say in words what the population proportion p is for this poll.

(b) Find a 95% confidence interval for p.

(c) Gallup announced a margin of error of plus or minus three percentage points for this poll result. How well does your work in

(b) agree with this margin of error?