Asample poll of 100 voters chosen at random from all voters in a given district indicated that 55 of them were in favor of a particular candidate. find the 99% confidence limits for the proportion of all voters in favor of this candidate.

The confidence interval for proportion is

Here

Using standard normal tables .

The 99% confidence interval for proportion is

The CI interpretation is that "We are 99% confident that the proportion of voters in favor of the candidate lies between 0.422 and 0.678".

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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