A caf records that in (n=81) cases, the coffee beans for the coffee machine lasted an average

A café records that in \(n=81\) cases, the coffee beans for the coffee machine lasted an average of 225 cups with a standard deviation of 22 cups.

(a) Obtain a 90\% confidence interval for \(\mu\), the population mean number of cups before the coffee machine needs to be refilled with beans.

(b) Does \(\mu\) lie in your interval obtained in part (a)? Explain.

(c) In a long series of repeated experiments, what proportions of the respective confidence intervals contain the true mean? Explain your reasoning.