4 In a rock, small crystal formations occur at a constant average rate of 3.2 per cubic metre.
- State a further assumption needed to model the number of crystal formations in a fixed volume of rock by a Poisson distribution.
In the remainder of the question, you should assume that a Poisson model is appropriate.
- Calculate the probability that in one cubic metre of rock there are exactly 5 crystal formations.
- Calculate the probability that in 0.74 cubic metres of rock there are at least 3 crystal formations.
- Use a suitable approximation to calculate the probability that in 10 cubic metres of rock there are at least 36 crystal formations.