Mei is investigating contamination in sets of 12 laboratory samples. She models the number of contaminated samples in a set by X∼B(12,0.10)X\sim B(12,0.10)X∼B(12,0.10).
Using Mei's model, find P(X≥3)P(X \ge 3)P(X≥3).
Mei examines 50 sets. Using the model, find the expected number of sets containing no contaminated samples.
Of the 50 sets, 15 contain no contaminated samples and 6 contain at least 3 contaminated samples. State, with a reason, whether these observations support Mei's model.
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.