Question 1 - A-Level Maths

CAIE S2 2020 November — Question 1 3 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2020
Session	November
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Poisson distribution
Type	Standard Poisson approximation to binomial
Difficulty	Moderate -0.5 This is a straightforward application of Poisson approximation to binomial with clearly stated parameters (n=150000, p=1/50000, giving λ=3). The calculation requires finding P(X>2)=1-P(X≤2) using standard Poisson tables or formula. While it involves Further Maths content, it's a routine textbook exercise with no conceptual challenges beyond recognizing when to use the approximation.
Spec	2.04d Normal approximation to binomial

1 On average, 1 in 50000 people have a certain gene.
Use a suitable approximating distribution to find the probability that more than 2 people in a random sample of 150000 have the gene.

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
Poisson, any \(\lambda\)	M1	Used
\(1 - e^{-3}\left(1 + 3 + \frac{3^2}{2}\right)\)	M1	Allow one end error
\(= 0.577\) (3sf)	A1	SC Use of Binomial (or unsupported correct answer) scores B1 only
3

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Poisson, any $\lambda$ | M1 | Used |
| $1 - e^{-3}\left(1 + 3 + \frac{3^2}{2}\right)$ | M1 | Allow one end error |
| $= 0.577$ (3sf) | A1 | SC Use of Binomial (or unsupported correct answer) scores B1 only |
| | **3** | |

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1 On average, 1 in 50000 people have a certain gene.\\
Use a suitable approximating distribution to find the probability that more than 2 people in a random sample of 150000 have the gene.\\

\hfill \mbox{\textit{CAIE S2 2020 Q1 [3]}}

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