19N.2.AHL.TZ0.H_2

pestleMathematicsAIHLPaper 219N· ahl-4-17-poisson-distributionsource ↗

The number of marathons that Audrey runs in any given year can be modelled by a Poisson distribution with mean 1.3 .

Calculate the probability that Audrey will run at least two marathons in a particular year.

[2]

Find the probability that she will run at least two marathons in exactly four out of the following five years.

[4]

Markscheme / solution

$X \sim {\text{Po}}\left( {1.3} \right)$

${\text{P}}\left( {X \geqslant 2} \right) = 0.373$ (M1)A1

[2 marks]

$V \sim {\text{B}}\left( {5{\text{, }}0.373} \right)$ (M1)A1

Note: Award (M1) for recognition of binomial or equivalent, A1 for correct parameters.

${\text{P}}\left( {V = 4} \right) = 0.0608$ (M1)A1

[4 marks]

Examiners’ report

[N/A]