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.
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.