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At the Fencing Center, 60% of fencers use the foil. Surveying 25 fencers at random, X ~ B(25, 0.40) counts those who do NOT use the foil. What is the expected number who do not use the foil?
A15 students, on average
B10 students, on average
C25 students, on average
D0.40 of a student
Answer & Solution
Correct answer: B. 10 students, on average
1. Since 60% use the foil, the remaining 40% do not, so p = 0.40 for the event of interest.
2. X, the number not using the foil among 25 fencers, is binomial with μ = np.
3. μ = (25)(0.40) = 10.
4. Option A applies the wrong percentage, and option D confuses the probability p with the expected count itself.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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