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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.