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40% of adults will watch the Super Bowl, so X ~ G(0.40) counts how many adults must be surveyed until one who will watch is found. What is the expected number of adults you must survey?
A0.40 adults, on average
B2.5 adults, on average
C0.60 adults, on average
D40 adults, on average
Answer & Solution
Correct answer: B. 2.5 adults, on average
1. For a geometric random variable, μ = 1/p.
2. Here p = 0.40, so μ = 1/0.40 = 2.5 adults.
3. On average you would need to survey 2.5 adults until finding one who plans to watch.
4. Options C and D confuse the probability of failure or the percentage itself with the expected count of trials.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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