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For the millennial social-media example, X ~ G(0.25) counts people asked until finding one without a profile, with μ = 4 and σ ≈ 3.4641. Using geometcdf, P(x≤5) = 0.7627. What does this cumulative probability represent?
AThe chance the first no-profile person is asked fifth
BThe chance that exactly five people have no profile
CThe chance that the mean of four gets exceeded
DThe chance that no one asked has any profile
Answer & Solution
Correct answer: A. The chance the first no-profile person is asked fifth
1. geometcdf(p, k) sums the geometric probabilities for x = 1 through x = k.
2. Here geometcdf(0.25, 5) adds P(x=1) through P(x=5), giving the chance the first success occurs on or before the fifth person asked.
3. That cumulative value is 0.7627.
4. Option B describes a single-value pmf outcome, not a cumulative sum, so it misreads the calculation.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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