The formula for the confidence interval is

Thus, the error in the confidence interval is

where we have s = 0.5, = 0.05, /2 = 0.025, z/2 = 1.96, s = 0.5. We are also required to come up with an error of no more than 0.1, and we are asked to estimate n. To do this, substitute these values in the formula and solve for n:

This gives

and so

Thus, to be absolutely shure the confidence interval is no wider than 0.1, you should round this up to 97 people (since 96 people would give an error slightly larger than 0.1). Thus, you should have at least 97 people in the survey.

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