18M.2.AHL.TZ1.H_6

pestleMathematicsAIHLPaper 218M· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

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 / solution

* 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)

$= \frac{{{\text{P}}\left( {X > 190} \right)}}{{{\text{P}}\left( {X \geqslant 168} \right)}} = \left( {\frac{{0.19827 \ldots }}{{0.80817 \ldots }}} \right)$ (A1)(A1)

= 0.245 A1

[5 marks]

Examiners’ report

[N/A]