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 .
- Determine the probability that, during a given 8 -hour period, the number of telephone calls received that request an urgent visit by an engineer is:
- at most 5 ;
- exactly 7 ;
- at least 5 but fewer than 10 .
- Write down the distribution for the number of telephone calls received each hour that request an urgent visit by an engineer.
- 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.
- 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.
(1 mark) - Calculate the probability that at 11 am an engineer will not be immediately available to make an urgent visit.
- Give a reason why a Poisson distribution may not be a suitable model for the number of telephone calls per hour received by the IT company that request an urgent visit by an engineer.
(1 mark)
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