In the survey being conducted to see whether Americans are in favor of the death penalty or not, 2815 people make up the sample size. In a survey, the accuracy of the result is reduced by the size of the sample. The sensitivity of the survey conducted in estimating the correct outcome can be arrived at as follows.

Take the desired sensitivity, here it is 95% or 0.95. Subtract this from 1, 1 - 0.95 = 0.05. Multiply the two values, 0.95*0.05 = 0.0475. Divide this by the sample size, here it is 2815, `0.0475/2815 ~~ 1.687*10^-5` . Take the square root of this value, `sqrt(0.0475/2815 ) ~~ 4.1077*10^-3` . For the 95% confidence interval the corresponding value in normal distribution tables is 1.96.

`4.1077*10^-3*1.96 = 8.05*10^-3`

The value obtained above added and subtracted from 0.95 provides the 95% confidence interval relevant to the survey outcome. It is 0.9580512 to 0.9419. The 95% confidence interval for the survey is 0.9580 to 0.9419