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# S2 poisson distribution watch

1. A car-hire firm finds that the daily demand for its cars follows a Poisson distribution with mean 3.6.
a) What is the probability that on a particular day the demand will be:
i) two or fewer,
ii) between three and seven (inclusive),
b) What is the probability that 10 consecutive days will include two or more on which the demand is zero?
I don't know how to do (b)
Thanks for the help
2. (Original post by -Ahmed-)
A car-hire firm finds that the daily demand for its cars follows a Poisson distribution with mean 3.6.
a) What is the probability that on a particular day the demand will be:
i) two or fewer,
ii) between three and seven (inclusive),
b) What is the probability that 10 consecutive days will include two or more on which the demand is zero?
I don't know how to do (b)
Thanks for the help
Whenever you see something with a fixed number of trials (i.e. 10 consecutive days) with a fixed chance of success P(X=0), the first thing that should spring to your mind is BINOMIAL DISTRIBUTION.

So first work out P(X=0) for the Po(3.5).

Then write out the statement Y~B(10, p) where p is the value you calculated for P(X=0) from above.

Then work out P(Y≥2) using your new binomial distribution statement.

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Updated: March 12, 2016
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