An engineer is monitoring the mass of precision-engineered lithium cells, $W\,$ grams, where $\sim \operatorname{N}(\mu, \sigma^2)$ .

A random sample of these cells is measured, yielding a 99% confidence interval for $\mu\,$ of $(142.34, 148.86)$ .

Find, to 2 decimal places, the standard error of the mean.

Hence, or otherwise, calculate a 90% confidence interval for $\mu\,$ based on this same sample of lithium cells.

For quality assurance, six independent random samples are taken, and a 90% confidence interval for $\mu\,$ is constructed for each.

Calculate the probability that at least 5 of these intervals will contain the true population mean $μ\mu$ .

An engineer is monitoring the mass of precision-engineered lithium cells, $W\,$ grams, where $\sim \operatorname{N}(\mu, \sigma^2)$ .

A random sample of these cells is measured, yielding a 99% confidence interval for $\mu\,$ of $(142.34, 148.86)$ .

Find, to 2 decimal places, the standard error of the mean.

Hence, or otherwise, calculate a 90% confidence interval for $\mu\,$ based on this same sample of lithium cells.

For quality assurance, six independent random samples are taken, and a 90% confidence interval for $\mu\,$ is constructed for each.

Calculate the probability that at least 5 of these intervals will contain the true population mean $μ\mu$ .

4.5.1 Statistical distributions (A-level only)

4.5.1 Statistical distributions (A-level only) Questions