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# Poisson distribution, question. I am Panicing watch

1. An indoor tennis centre has five courts which are booked by members of the public, usually over the telephone.

Demand for each hour in the peak-period hours, i.e. 4pm to 11pm, has been found to rise to a Poisson distribution with a mean of 9 if the tennis centre continues to charge its off-peak rate of £6 per court per hour. The centre management is therefore considering setting the price at a higher level during the peak period. In fact they have experimented with different prices and have found the following demand levels:

Price (per ct per hr) | Mean Hourly Demand
£6 _____________|______9
£7 _____________|______8
£8 _____________|______7
£9 _____________|______6
£10 _____________|______5
£11 _____________|______4
£12 _____________|______3

(i) What proportion of demand would be turned away if the peak-period price is set at the current off-peak price of £6 per court per hour, and what hourly income would be generated?

(ii) At what level should they set the peak-period price in order to maximise the average hourly income during the peak period?

I don't know What method to use, to solve it...
2. draw a poisson curve with peak the mean, draw a line through it at 5. find area under curve.

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