CAIE S2 2017 November — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2017
SessionNovember
Marks3
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Mark schemeDownload PDF ↗
TopicApproximating the Poisson to the Normal distribution
TypeSimple probability using normal approximation
DifficultyModerate -0.8 This is a straightforward application of a standard approximation technique. Students need only recall that Po(λ) ≈ N(λ, λ), apply continuity correction (X > 40 becomes X > 40.5), standardize to find z = (40.5-31)/√31 ≈ 1.71, and look up the normal table. It's routine recall with minimal problem-solving, easier than average A-level questions.
Spec2.04d Normal approximation to binomial
1 A random variable, \(X\), has the distribution \(\operatorname { Po } ( 31 )\). Use the normal approximation to the Poisson distribution to find \(\mathrm { P } ( X > 40 )\).
Question 1:
AnswerMarks Guidance
AnswerMark Guidance
\(\frac{40.5-31}{\sqrt{31}}\) \((= 1.706)\)M1 standn correct but allow with no or incorrect cc
\(1 - \phi(\text{"1.706"})\)M1 indep correct area consistent with working
\(= 0.0441\) (3 sf) or \(0.0440\)A1 not \(0.044\)
Total: 3 
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{40.5-31}{\sqrt{31}}$ $(= 1.706)$ | M1 | standn correct but allow with no or incorrect cc |
| $1 - \phi(\text{"1.706"})$ | M1 | indep correct area consistent with working |
| $= 0.0441$ (3 sf) or $0.0440$ | A1 | not $0.044$ |
| **Total: 3** | | |

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1 A random variable, $X$, has the distribution $\operatorname { Po } ( 31 )$. Use the normal approximation to the Poisson distribution to find $\mathrm { P } ( X > 40 )$.\\

\hfill \mbox{\textit{CAIE S2 2017 Q1 [3]}}
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