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75% of millennials have a profile on a social networking site. Let X ~ G(0.25) count how many millennials you must ask until you find one WITHOUT a profile. Using geometpdf, P(x=10) = 0.0188. What does this represent?
AThat exactly ten people surveyed have no profile
BThat fewer than ten people were asked in total
CThat person ten is the first one with no profile
DThe expected number of people you must ask
Answer & Solution
Correct answer: C. That person ten is the first one with no profile
1. Here 'success' is finding a person without a profile, so p = 1 - 0.75 = 0.25.
2. X ~ G(0.25) counts the number of people asked, including the successful one, until that first success.
3. P(x=10) = geometpdf(0.25, 10) = 0.0188 means the first no-profile person shows up exactly on the tenth person asked.
4. Option D describes the mean, 1/0.25 = 4, which is a different quantity from P(x=10).
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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