CAIE S2 2021 November — Question 2 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicApproximating the Poisson to the Normal distribution
TypeSimple probability using normal approximation
DifficultyModerate -0.3 This is a straightforward application of the normal approximation to the Poisson distribution. Students need to recognize when to use the approximation (large λ), apply continuity correction, standardize to find P(X > 60), and use normal tables. While it requires multiple steps, each is routine for S2 level with no conceptual challenges or novel problem-solving required.
Spec2.04d Normal approximation to binomial5.02i Poisson distribution: random events model

2 The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all. Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received.

Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\(N(45.2,\ 45.2)\)B1 SOI
\(\frac{60.5 - 45.2}{\sqrt{45.2}} = 2.276\)M1 Allow with wrong or no continuity correction.
\(1 - \phi(2.276)\)M1
\(0.0114\)A1
Total: 4
**Question 2:**

| Answer | Mark | Guidance |
|--------|------|----------|
| $N(45.2,\ 45.2)$ | B1 | SOI |
| $\frac{60.5 - 45.2}{\sqrt{45.2}} = 2.276$ | M1 | Allow with wrong or no continuity correction. |
| $1 - \phi(2.276)$ | M1 | |
| $0.0114$ | A1 | |
| | **Total: 4** | |
2 The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are received in a day, the customer service desk cannot deal with them all.

Use a suitable approximating distribution to find the probability that, on a randomly chosen day, the customer service desk cannot deal with all the enquiries that are received.\\

\hfill \mbox{\textit{CAIE S2 2021 Q2 [4]}}