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 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.