The weights of mineral samples, W W\,W grams, collected by a deep-sea drone are normally distributed with an unknown mean μ \mu\,μ and a known variance σ2\sigma^2σ2. Based on a random sample of n n\,n observations of WWW, a 90% confidence interval for μ \mu\,μ was calculated as (45.32,46.18)(45.32, 46.18)(45.32,46.18).
Show that the standard error of the mean calculated from this sample is 0.261 to 3 significant figures.
Using the same random sample,
determine a 99% confidence interval for μ\muμ. Give your limits to 3 decimal places.
A different r% r\%\,r% confidence interval for μ \mu\,μ constructed from this same sample has a total width of 1.20 grams.
Calculate the value of rrr.
