A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence?Find the z-table here.

For a population proportion, use n = z²p(1 − p)/E². At 95% confidence, z = 1.96; here p = 0.61 and the desired margin of error is E = 0.03. Substituting gives n = (1.96²)(0.61)(0.39)/(0.03²) ≈ 1,015.47. Round up to ensure the margin of error is at most 0.03, so the answer is 1,016 constituents.

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