An engineer is monitoring the mass of precision-engineered lithium cells, W W\,W grams, where W∼N(μ,σ2)W \sim \operatorname{N}(\mu, \sigma^2)W∼N(μ,σ2).
A random sample of these cells is measured, yielding a 99% confidence interval for μ \mu\,μ of (142.34,148.86)(142.34, 148.86)(142.34,148.86).
Find, to 2 decimal places, the standard error of the mean.
Hence, or otherwise, calculate a 90% confidence interval for μ \mu\,μ based on this same sample of lithium cells.
For quality assurance, six independent random samples are taken, and a 90% confidence interval for μ \mu\,μ is constructed for each.
Calculate the probability that at least 5 of these intervals will contain the true population mean μ\muμ.
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.