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A men's soccer team plays zero days a week with probability 0.2, one day with probability 0.5, and two days with probability 0.3. What is the expected number of days per week the team plays, μ?
Aμ = 1.1
Bμ = 1.0
Cμ = 0.5
Dμ = 1.5
Answer & Solution
Correct answer: A. μ = 1.1
1. Build the x times P(x) column: (0)(0.2) = 0, (1)(0.5) = 0.5, and (2)(0.3) = 0.6.
2. Add the column: 0 + 0.5 + 0.6 = 1.1.
3. This sum is μ, so the expected number of playing days per week is 1.1.
4. Option B uses only the middle term, and options C and D do not match the weighted sum, so they are distractors.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.2 Mean or Expected Value and Standard Deviation_
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