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.
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.