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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.