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QuizMultiple Choice

Estimating a Population Proportion

Question 1 • CA-Statistics and Probability B

A scientist wants to sample fish from a large aquarium to estimate the true proportion of striped fish. How many fish are required for a random sample to obtain a margin of error of at most 0.06 with 95% confidence?Find the z-table here.

Answer
A
188
B
267
C
278
D
461

Explanation

For a proportion, use the conservative estimate p = 0.50 when the true proportion is unknown; this gives the largest required sample. With 95% confidence, z = 1.96, and the margin of error is 0.06: n = (1.96² × 0.50 × 0.50) / 0.06² ≈ 266.78. Round up to ensure the margin of error is no more than 0.06, so 267 fish are needed (choice B).

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