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 (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.