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Date May 2018 Marks available 5 Reference code 18M.2.AHL.TZ1.H_6
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Calculate Question number H_6 Adapted from N/A

Question

The mean number of squirrels in a certain area is known to be 3.2 squirrels per hectare of woodland. Within this area, there is a 56 hectare woodland nature reserve. It is known that there are currently at least 168 squirrels in this reserve.

Assuming the population of squirrels follow a Poisson distribution, calculate the probability that there are more than 190 squirrels in the reserve.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

X is number of squirrels in reserve
X ∼ Po(179.2)      A1

Note: Award A1 if 179.2 or 56 × 3.2 seen or implicit in future calculations.

recognising conditional probability     M1

P(X > 190 | X ≥ 168)

= P ( X > 190 ) P ( X 168 ) = ( 0.19827 0.80817 )        (A1)(A1)

= 0.245      A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
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Topic 4—Statistics and probability » SL 4.8—Binomial distribution
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Topic 4—Statistics and probability

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