Date | November Example question | Marks available | 6 | Reference code | EXN.1.AHL.TZ0.16 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | 16 | Adapted from | N/A |
Question
The cars for a fairground ride hold four people. They arrive at the platform for loading and unloading every 30 seconds.
During the hour from 9 am the arrival of people at the ride in any interval of t minutes can be modelled by a Poisson distribution with a mean of 9t (0<t<60).
When the 9 am car leaves there is no one in the queue to get on the ride.
Shunsuke arrives at 9.01 am.
Find the probability that more than 7 people arrive at the ride before Shunsuke.
Find the probability there will be space for him on the 9.01 car.
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
Let X be the number of people who arrive between 9.00 am and 9.01 am
X~Po(9)
P(X>7)=P(X≥8) (M1)
0.676 A1
[2 marks]
Mean number of people arriving each seconds is (M1)
Let be the number who arrive in the first seconds and the number who arrive in the second seconds.
(Shunsuke will be able to get on the ride)
M1M1
Note: M1 for first term, M1 for any of the other terms.
null (A1)(A1)
Note: (A1) for one correct value, (A1)(A1) for four correct values.
A1
[6 marks]