The electrical resistance of a batch of specialized superconducting components, R R\,R ohms, follows a normal distribution such that R∼N(μ,0.82)R \sim \text{N}(\mu, 0.8^2)R∼N(μ,0.82).
It is known that 20% of these components have a resistance exceeding 100.5 ohms. Determine the value of μ \mu\,μ to the nearest 0.1 ohm.
A technician randomly selects 12 components from the batch for testing.
Find the probability that fewer than 2 of these components have a resistance exceeding 100.5 ohms.
A large-scale circuit assembly requires 150 of these components selected at random.
Using a suitable approximation, find the probability that more than 35 of these components have a resistance exceeding 100.5 ohms.
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.