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.

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]