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For the Afghanistan literacy example, X ~ B(15, 0.281) gives P(x=3) = 0.1927 and P(x=4) = 0.2259. Is it more likely that three or four of the 15 sampled people are literate?
AThree, since P(x=3) is the larger probability
BBoth are equally likely outcomes
CFour, since P(x=4) is the larger probability
DNeither is possible under this distribution
Answer & Solution
Correct answer: C. Four, since P(x=4) is the larger probability
1. Compare the two probabilities: P(x=3) = 0.1927 and P(x=4) = 0.2259.
2. 0.2259 is greater than 0.1927.
3. So it is more likely that four of the fifteen people sampled are literate.
4. Option B ignores the numeric difference between the two probabilities, and option D contradicts the fact that both values are legitimate binomial probabilities.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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