Date | May 2021 | Marks available | 2 | Reference code | 21M.2.AHL.TZ2.5 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | 5 | Adapted from | N/A |
Question
Hank sets up a bird table in his garden to provide the local birds with some food. Hank notices that a specific bird, a large magpie, visits several times per month and he names him Bill. Hank models the number of times per month that Bill visits his garden as a Poisson distribution with mean .
Over the course of consecutive months, find the probability that Bill visits the garden:
Using Hank’s model, find the probability that Bill visits the garden on exactly four occasions during one particular month.
on exactly occasions.
during the first and third month only.
Find the probability that over a -month period, there will be exactly months when Bill does not visit the garden.
After the first year, a number of baby magpies start to visit Hank’s garden. It may be assumed that each of these baby magpies visits the garden randomly and independently, and that the number of times each baby magpie visits the garden per month is modelled by a Poisson distribution with mean .
Determine the least number of magpies required, including Bill, in order that the probability of Hank’s garden having at least magpie visits per month is greater than .
Markscheme
A1
[1 mark]
(M1)
A1
[2 marks]
(M1)
(A1)
A1
[3 marks]
(A1)
(M1)(A1)
Note: Award M1 for recognizing binomial probability, and A1 for correct parameters.
A1
[4 marks]
METHOD ONE
(M1)(A1)(A1)
Note: Award M1 for evidence of a cumulative Poisson with , A1 for and A1 for .
so require magpies (including Bill) A1
METHOD TWO
evidence of a cumulative Poisson with (M1)
sketch of curve and (A1)
(intersect at) (A1)
rounding up gives
so require magpies (including Bill) A1
[4 marks]