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.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.