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A Level Stats poisson distribution question

I'm having difficulty answering this:

A ferry takes cars and small vans on a short journey from an island to the
mainland. On a representative sample of weekday mornings, the numbers of
vehicles, X, on the 8 am sailing were as follows.
20 24 24 22 23 21 20 22 23 22
21 21 22 21 23 22 20 22 20 24
(i) Show that X does not have a Poisson distribution.
In fact 20 of the vehicles belong to commuters who use that sailing of the ferry
every weekday morning. The random variable Y is the number of vehicles
other than those 20 who are using the ferry.
(ii) Investigate whether Y may reasonably be modelled by a Poisson
distribution.
The ferry can take 25 vehicles on any journey.
(iii) On what proportion of days would you expect at least one vehicle to be
unable to travel on this particular sailing of the ferry because there was no
room left and so have to wait for the next one?

I understand (i) and (ii) but am not sure on (iii)
Thanks !
Reply 1
Original post by zolearns
I'm having difficulty answering this:

A ferry takes cars and small vans on a short journey from an island to the
mainland. On a representative sample of weekday mornings, the numbers of
vehicles, X, on the 8 am sailing were as follows.
20 24 24 22 23 21 20 22 23 22
21 21 22 21 23 22 20 22 20 24
(i) Show that X does not have a Poisson distribution.
In fact 20 of the vehicles belong to commuters who use that sailing of the ferry
every weekday morning. The random variable Y is the number of vehicles
other than those 20 who are using the ferry.
(ii) Investigate whether Y may reasonably be modelled by a Poisson
distribution.
The ferry can take 25 vehicles on any journey.
(iii) On what proportion of days would you expect at least one vehicle to be
unable to travel on this particular sailing of the ferry because there was no
room left and so have to wait for the next one?

I understand (i) and (ii) but am not sure on (iii)
Thanks !


Youd want to work out the cumulative P(Y>5). Generally a sketch of the distribution and the value(s) of interest helps.
Reply 2
Okay, thanks

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