Question about confidence intervals (intro stats)

[kingofmirrors]

Say there's a project that will only get approved if 80% of the people polled support it. You gather some sample data and create a confidence interval that comes out to (50%, 90%). Why can't you then say that based on the confidence interval there is a 25% {(.9-.8)/(.9-.5)} chance the project will be approved?

(note: if you can, it was my stats teacher who said you couldn't, but didn't bother to explain why not).

[Drag]

That depends on the distribution of the data. As far as I understand in such a problem we usually assume a Gaussian distribution with a mean of 70% and SD of 20% and integrate it from 80% to infinity you'll get a number which won't be equal 1/4.