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In a 560-page art catalog, 8 pages feature signature artists. Sampling 100 pages gives X ~ B(100, 8/560). Using a binomial calculator, P(x=2) = 0.2466 and P(x≤6) = 0.9994. What is P(x>3), the probability that more than three sampled pages feature signature artists?
A0.0557
B0.9994
C0.2466
D0.9443
Answer & Solution
Correct answer: A. 0.0557
1. P(x>3) is the complement of P(x≤3), so P(x>3) = 1 - P(x≤3).
2. A binomial calculator gives P(x≤3) = 0.9443 for X ~ B(100, 8/560).
3. So P(x>3) = 1 - 0.9443 = 0.0557.
4. Option D is P(x≤3) itself, not its complement, and option B is P(x≤6), a different event entirely.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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