Batches of specialized coffee beans are monitored for a rare quality trait called 'extra-large' size after roasting. Historical data indicates that the probability of a bean being extra-large is 0.015.
Write down a suitable model for the distribution of the number of extra-large beans in a batch of n n\,n beans.
State one assumption required for this model to be valid in this context.
Using a suitable approximation, find the probability that exactly 7 out of 400 beans in a random batch are identified as being extra-large.
Explain why the approximation used in part (c) is appropriate.
A head barista claims that 70% of regular customers prefer oat milk over dairy milk in their lattes.
In a random sample of 150 regular customers, it is found that 92 prefer oat milk.
Using a suitable approximation, test the barista's claim at the 5% significance level. State your hypotheses clearly.
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.