A botanical garden offers a "rare bloom" seed in 15% of its wildflower packets. No packet contains more than one rare bloom seed. Packets are sold in wholesale bundles of 12.
(i) Suggest a suitable distribution to model the number of rare bloom seeds, SSS, found in a single bundle. (ii) State one necessary assumption for this model to be valid.
Calculate the probability that out of 3 randomly selected bundles, exactly 1 bundle contains exactly 2 rare bloom seeds.
Determine the probability that a randomly selected bundle contains at least 3 rare bloom seeds.
A regional distributor buys 120 bundles for a seasonal sale.
Using a normal approximation, find the probability that fewer than 25 of these bundles contain at least 3 rare bloom 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.