S2 help!! Poisson and discrete variablesWatch
5) The number of telephone calls received, during an 8-hour period, by an IT company that request an urgent visit by an engineer may be modelled by a Poisson distribution with a mean of 7 .
The IT company has 4 engineers available for urgent visits and it may be assumed that each of these engineers takes exactly 1 hour for each such visit.
At 10 am on a particular day, all 4 engineers are available for urgent visits.
(i) State the maximum possible number of telephone calls received between 10 am and 11 am that request an urgent visit and for which an engineer is immediately available.
(ii) Calculate the probability that at 11 am an engineer will not be immediately available to make an urgent visit
Obviously part i) is 4 however part ii) is confusing me. In my head it is asking for the probability that all 4 engineers are called out in the hour before 11am so that none are available at 11am. So I calculated
P(X=4) = e^0.875 x (0.875^4/4!) = 0.0102
but the mark scheme disagrees and I can't figure out where it's coming from.
Also, question 6) b) iii) http://filestore.aqa.org.uk/subjects...W-QP-JUN10.PDF (can't figure out how to copy and paste the tables)
I can do the rest of the question but these 'given that' probabilities confuse me when they have probabilities within them. Help please?
Mark scheme is here: http://filestore.aqa.org.uk/subjects...W-MS-JUN10.PDF
I'm also stuck on a similar q haha