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Text message users send or receive an average of 41.5 texts per day. Converted to an hourly rate of about 1.7292 texts per hour, X ~ P(1.7292). What is P(x=2), the probability of exactly two texts in an hour?
A0.7495
B0.2505
C0.2653
D1.7292
Answer & Solution
Correct answer: C. 0.2653
1. Rescale the daily rate to an hour: 41.5/24 ≈ 1.7292 texts per hour, so X ~ P(1.7292).
2. Apply the Poisson pmf: P(x=2) = poissonpdf(1.7292, 2).
3. This evaluates to about 0.2653.
4. Option A is P(x≤2), a cumulative probability, and option C is P(x>2), the complement of that cumulative value, neither of which is P(x=2).
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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