The concentration of a rare-earth element in a soil sample, denoted by the random variable CCC, follows a normal distribution with an unknown mean μ\muμ and a known variance σ2\sigma^2σ2. A geologist collects a random sample of nnn measurements of CCC, which results in a 90%90\%90% confidence interval for μ\muμ of (45.82,47.18)(45.82, 47.18)(45.82,47.18).
Show that the standard error of the mean calculated from this sample is 0.4130.4130.413 to 333 significant figures.
Using the same random sample,
find a 99%99\%99% confidence interval for μ\muμ. Give your limits to 333 decimal places.
The r%r\%r% confidence interval calculated from the same sample data has a total width of 1.801.801.80.
Calculate the value of rrr, giving your answer to 111 decimal place.