6. A biologist is studying the behaviour of sheep in a large field. The field is divided up into a number of equally sized squares and the average number of sheep per square is 2.25 . The sheep are randomly spread throughout the field.

1. Suggest a suitable model for the number of sheep in a square and give a value for any parameter or parameters required. Calculate the probability that a randomly selected sample square contains
2. no sheep,
3. more than 2 sheep. A sheepdog has been sent into the field to round up the sheep.
4. Explain why the model may no longer be applicable. In another field, the average number of sheep per square is 20 and the sheep are randomly scattered throughout the field.
5. Using a suitable approximation, find the probability that a randomly selected square contains fewer than 15 sheep.