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.
