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 (suggested by the article “An Example of Good but Partially Successful OR Engagement: Improving Outpatient Clinic Operations,” Interfaces 28, #5).

a. Calculate and interpret a 95% upper confidence bound for true average waiting time. 

b. Based on the sample mean and standard deviation, why is it doubtful that the population of waiting times is normally distributed? Does that invalidate the confidence bound you calculated in part (a)?