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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.