- A botanist is studying the distribution of daisies in a field. The field is divided into a number of equal sized squares. The mean number of daisies per square is assumed to be 3. The daisies are distributed randomly throughout the field.
Find the probability that, in a randomly chosen square there will be
- more than 2 daisies,
- either 5 or 6 daisies.
The botanist decides to count the number of daisies, \(x\), in each of 80 randomly selected squares within the field. The results are summarised below
$$\sum x = 295 \quad \sum x ^ { 2 } = 1386$$
- Calculate the mean and the variance of the number of daisies per square for the 80 squares. Give your answers to 2 decimal places.
- Explain how the answers from part (c) support the choice of a Poisson distribution as a model.
- Using your mean from part (c), estimate the probability that exactly 4 daisies will be found in a randomly selected square.