3. A botanist suggests that the number of a particular variety of weed growing in a meadow can be modelled by a Poisson distribution.
- Write down two conditions that must apply for this model to be applicable.
Assuming this model and a mean of 0.7 weeds per \(\mathrm { m } ^ { 2 }\), find
- the probability that in a randomly chosen plot of size \(4 \mathrm {~m} ^ { 2 }\) there will be fewer than 3 of these weeds.
- Using a suitable approximation, find the probability that in a plot of \(100 \mathrm {~m} ^ { 2 }\) there will be more than 66 of these weeds.
(6)