A random sample of 50 patients who had been seen at an outpatient clinic was selected, and the waiting time to see a physician was determined for each one, resulting in a sample mean time of 40.3 min and a sample standard deviation of 28.0 min.

Construct an 95% confidence interval of the true average waiting time.

Assuming it is known that the true standard deviation of the waiting time is 27 min, construct an 95% confidence interval of the true average waiting time.