The observations on escape time given in Exercise 36 of Chapter 1 give a sample mean and sample standard deviation of 370.69 and 24.36, respectively.

a. Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.

b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%. How does this bound compare with the confidence bound of part (a)?

c. Suppose that two additional workers will be chosen to participate in the simulated escape exercise. Denote their escape times by X27 and X28, and let denote the average of these two values. Modify the formula for a PI for a single x value to obtain a PI for , and calculate a 95% two-sided interval based on the given escape data.