The number of eggs laid by an insect follows a Poisson distribution with parameter 200.

(a) Find the probability that (i) more than 170 eggs are laid, (ii) more than 205 eggs are laid, (iii) between 180 and 240 eggs (inclusive) are laid.

(b) If the probability that an egg develops is 0.1, show that the number of survivors follows a Poisson distribution with parameter 20 and find the probability thus there are more than 30 survivors.