CAIE S2 2016 November — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2016
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPoisson distribution
TypeSingle time period probability
DifficultyEasy -1.2 This is a straightforward application of the Poisson distribution requiring only calculator use or table lookup to find P(X < 3) = P(X ≤ 2). It involves no problem-solving, conceptual understanding beyond basic probability notation, or multi-step reasoning—purely routine computation with a given parameter.
Spec5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities
1 The random variable \(X\) has the distribution \(\operatorname { Po } ( 3.5 )\). Find \(\mathrm { P } ( X < 3 )\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(e^{-3.5}(1 + 3.5 + \frac{3.5^2}{2!})\)M2 Allow M1 if extra term \(e^{-3.5} \times \frac{3.5^3}{3!}\) or "\(1 - \)." or omit \(P(0)\)
\(= 0.321\) (3 sf)A1 [3] 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $e^{-3.5}(1 + 3.5 + \frac{3.5^2}{2!})$ | M2 | Allow M1 if extra term $e^{-3.5} \times \frac{3.5^3}{3!}$ or "$1 - $." or omit $P(0)$ |
| $= 0.321$ (3 sf) | A1 | [3] |

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1 The random variable $X$ has the distribution $\operatorname { Po } ( 3.5 )$. Find $\mathrm { P } ( X < 3 )$.

\hfill \mbox{\textit{CAIE S2 2016 Q1 [3]}}
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