CAIE S2 2018 June — Question 3 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2018
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicApproximating the Poisson to the Normal distribution
TypeScaled Poisson over time period
DifficultyStandard +0.3 This is a straightforward application of the normal approximation to Poisson with scaling. Students must recognize that 300 days means λ = 5.1 × 30 = 153, apply the normal approximation Po(153) ≈ N(153, 153), use continuity correction (P(X < 140) = P(X ≤ 139.5)), and standardize. While it requires multiple steps, each is routine for S2 level with no novel insight needed—slightly easier than average due to clear structure.
Spec2.04d Normal approximation to binomial5.02i Poisson distribution: random events model

3 The number of e-readers sold in a 10-day period in a shop is modelled by the distribution \(\operatorname { Po } ( 5.1 )\). Use an approximating distribution to find the probability that fewer than 140 e-readers are sold in a 300-day period.

Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
\(N(153, 153)\)B1 Seen or implied
\(\frac{139.5 - 153}{\sqrt{"153"}} \;(= -1.091)\)M1 Allow with wrong or no cc
\(\phi("-1.091") = 1 - \phi("1.091")\)M1 For area consistent with their working
\(= 0.138\) (3 sf)A1
**Question 3:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $N(153, 153)$ | B1 | Seen or implied |
| $\frac{139.5 - 153}{\sqrt{"153"}} \;(= -1.091)$ | M1 | Allow with wrong or no cc |
| $\phi("-1.091") = 1 - \phi("1.091")$ | M1 | For area consistent with their working |
| $= 0.138$ (3 sf) | A1 | |

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3 The number of e-readers sold in a 10-day period in a shop is modelled by the distribution $\operatorname { Po } ( 5.1 )$. Use an approximating distribution to find the probability that fewer than 140 e-readers are sold in a 300-day period.\\

\hfill \mbox{\textit{CAIE S2 2018 Q3 [4]}}