A biologist gathers leaves of a certain plant in order to collect insects of a particular type. From past experience she knows that the distribution of the number of insects on a leaves may be modelled by a Poisson distribution with mean 0.8.

(a) Calculate, to three decimal places, the probability that the number of insects on the next leaf to be examined will be fewer than three.

(b) Determine, to three decimal places, the probability that the total number of insects on the next ten leaves to be examined will lie between six and 12 (both inclusive).

(c) Use a distributional approximation to find, to two decimal places, the probability that the total number of insects on the next 50 leaves to be examined will exceed 45. (NEAB)