An agricultural inspector finds that 18% of cocoa trees in a large plantation have been affected by a particular fungal spore.
State a distribution that is suitable to model the number of affected trees in a random sample of 50 trees.
State two conditions for the distribution in part (a) to be a valid model.
Find the probability that:
exactly 10 trees in a sample of 50 are affected,
Find the probability that:
fewer than 4 trees in a random sample of 25 trees are affected.
A regional agriculture officer notes that resources will be strained if more than 160 trees are found to be affected in a specific plantation block containing 800 trees.
Using a suitable approximation, find the probability that resources will be strained in a particular plantation block.
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.