An industrial engineer concerned with service at a large medical clinic recorded the duration of time from the time a patient called until a doctor or nurse returned the call. A sample of size 180 calls had a mean of 1.65 hours and a standard deviation of 0.82 .

(a) Obtain a 95\% confidence interval for the population mean of time to return a call.

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

(c) In a long series or repeated experiments, with new random samples collected for each experiment, what proportion of the resulting confidence intervals will contain the true population mean? Explain your reasoning.