21M.1.AHL.TZ1.1

pestleMathematicsAIHLPaper 121M· ahl-4-17-poisson-distributionsource ↗

George goes fishing. From experience he knows that the mean number of fish he catches per hour is $1.1$ . It is assumed that the number of fish he catches can be modelled by a Poisson distribution.

On a day in which George spends $8$ hours fishing, find the probability that he will catch more than $9$ fish.

Markscheme / solution

$X ~ Po (8.8)$ (M1)

Note: Award (M1) for calculating the mean, $8.8$ , of the distribution

$P (X > 9) = P (X \geq 10)$ OR $P (X > 9) = 1 - P (X \leq 9)$ (M1)

$P (X > 9) = 0.386 (0.386260 \dots)$ (M1)A1

Note: Award (M1)(M0)(M1)A0 for finding $P (X \geq 9) = 0.518 (0.517719 \dots)$ OR $P (X \leq 9) = 0.614 (0.613740 \dots)$ .

[4 marks]

Examiners’ report

[N/A]