A botanist investigates the germination of a rare species of wildflower. It is known that, under specific laboratory conditions, each seed has a 25% probability of germinating successfully. The seeds are prepared in incubation trays, with each tray containing exactly 12 seeds.
(i) Suggest a suitable distribution to model the number of seeds that germinate in a single tray. (ii) State one necessary assumption for this model to be valid.
Calculate the probability that, in 2 randomly selected incubation trays, exactly 1 tray contains exactly 4 germinated seeds.
Calculate the probability that a randomly selected incubation tray contains at least 5 germinated seeds.
The botanist prepares a large-scale study involving 150 incubation trays.
Using a normal approximation, determine the probability that more than 20 of these trays contain at least 5 germinated seeds.
