A-LevelMathematicsProbability and statistics9709/63 · May/June 2021 · Q15 Marks
The number of goals scored by a team in a match is independent of other matches, and is denoted by the random variable X, which has a Poisson distribution with mean 1.36. A supporter offers to make a donation of $5 to the team for each goal that they score in the next 10 matches. Find the expectation and standard deviation of the amount that the supporter will pay.
- Find the expectation and standard deviation of the amount that the supporter will pay.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] λ = 10 × 1.36 [= 13.6]
- [A1] E(amount) = 5 × 13.6 = [$]68
- [M1] Var(amount) = 5² × 13.6 [= 340]
- [A1] Standard Deviation = [$]18.4(4) (3 s.f.) CAO condone 2√85
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