Question 1 - A-Level Maths

CAIE S2 2021 June — Question 1 4 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2021
Session	June
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Poisson distribution
Type	Scaled time period sums
Difficulty	Standard +0.3 This is a straightforward application of Poisson distribution properties: recognizing that independent Poisson variables sum to another Poisson, calculating the combined rate (2×(3.1+1.7)=9.6), and finding P(X>3)=1-P(X≤3) using tables or calculation. It requires standard technique with no novel insight, making it slightly easier than average.
Spec	5.02i Poisson distribution: random events model 5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities 5.02n Sum of Poisson variables: is Poisson

Accidents at two factories occur randomly and independently. On average, the numbers of accidents per month are 3.1 at factory \(A\) and 1.7 at factory \(B\). Find the probability that the total number of accidents in the two factories during a 2-month period is more than 3. [4]

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Question 1:

Answer	Marks	Guidance
1	λ = (3.1 + 1.7) × 2	M1
= 9.6	A1	Correct mean

1 – e–9.6 (1 + 9.6 + 9.62 + 9.63)

Answer	Marks	Guidance
2 3!	M1	Allow incorrect mean. Allow one end error.
= 0.986 (3 sf)	A1	SC If 9.6 seen and unsupported 0.986 M1A1B1.

SC Unsupported correct answer of 0.986 only if 9.6

also not seen scores B2 only.

4

Answer	Marks	Guidance
Question	Answer	Marks

Question 1:
1 | λ = (3.1 + 1.7) × 2 | M1 | Attempt combined mean. Allow 3.1 + 1.7 for M1
= 9.6 | A1 | Correct mean
1 – e–9.6 (1 + 9.6 + 9.62 + 9.63)
2 3! | M1 | Allow incorrect mean. Allow one end error.
= 0.986 (3 sf) | A1 | SC If 9.6 seen and unsupported 0.986 M1A1B1.
SC Unsupported correct answer of 0.986 only if 9.6
also not seen scores B2 only.
4
Question | Answer | Marks | Guidance

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Accidents at two factories occur randomly and independently. On average, the numbers of accidents per month are 3.1 at factory $A$ and 1.7 at factory $B$.

Find the probability that the total number of accidents in the two factories during a 2-month period is more than 3. [4]

\hfill \mbox{\textit{CAIE S2 2021 Q1 [4]}}

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