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# Statistic question watch

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

(a) It has been found that demand for courts in each off-peak hour, i.e. between 9am and 4pm, has a Poisson distribution with a mean of 4.
(i) What is the probability that none of the courts are booked between 10am and 11am on a particular day?
(ii) What is the probability that all five courts are booked between 10am and 11am on a particular day?
(iii) What is the probability that none of the courts are booked for exactly three of the off-peak hours on a particular day?
(iv) What is the probability that all 5 courts are booked for at least 5 of the off-peak hours?

I got

(1) 0.01832
(2) 0.15629
Is that correct?

And haven't got a clue, haow to start (3) or (4) need help please

Cheers
2. I don't have a calculator handy so I can't check 1) and 2).

For iii) and iv), a small hint is that you're going to need the Binomial distribution. A larger hint:

Spoiler:
Show
X ~ B(7, p), where p is the probability of no courts being booked in any given hour (or "successes" ), and there are 7 off peak hours in a day ("trials" ).
3. (Original post by tommm)
I don't have a calculator handy so I can't check 1) and 2).

For iii) and iv), a small hint is that you're going to need the Binomial distribution. A larger hint:

Spoiler:
Show
X ~ B(7, p), where p is the probability of no courts being booked in any given hour (or "successes" ), and there are 7 off peak hours in a day ("trials" ).
Ok I get your point. But shouldn't n=8, from 9am to 4 pm is eight hours, If I am not mistaken. thus X~B(8,p).

Also is the p for (3) Probability of none courts booked within an hour?

Same for the (4) but for all five booked?

Thank yo

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