A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. The population standard deviation is unknown. An investigation committee randomly surveyed 51 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours. a. Which distribution should you use for this problem (Normal or Student's t distribution)? Why? b. Construct a 99% confidence interval for the population mean time spent waiting. State the confidence interval and sketch the graph. c. Interpret the confidence interval.