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Using p' = q' = 0.5, z(0.05) = 1.645 for 90% confidence, and a target error bound of EBP = 0.03, the formula n = z^2*p'q'/EBP^2 gives n ≈ 751.7 customers aged 50+. How many customers should the company survey?
A751 customers
B1,645 customers
C752 customers
D300 customers
Answer & Solution
Correct answer: C. 752 customers
1. n = (1.645)^2 (0.5)(0.5) / (0.03)^2 ≈ (2.706)(0.25)/0.0009 ≈ 751.7.
2. Sample sizes always round up to the next whole number to guarantee the target precision.
3. Rounding 751.7 up gives n = 752 customers.
4. Option A rounds down instead of up, which would leave the survey slightly short of the required precision.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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