A group of human factor researchers are concerned about reaction to a stimulus by airplane pilots with a certain cockpit arrangement. An experiment was conducted in a simulation laboratory and 15 pilots were used with average reaction time 3.2 seconds and sample standard deviation 0.6 seconds, it is of interest to characterize extremes (i.e., worst case scenario). To that end, answer the following:

(a) Give a particular important one-sided 99% confidence bound on the mean reaction time. What assumption, if any, must you make on the distribution of reaction time?

(b) Give a 99% one-sided prediction interval and give an interpretation of what it means. Must you make an assumption on the distribution of reaction time to compute this bound?

(c) Compute a one-sided tolerance bound with 99% confidence that involves 95% of reaction times. Again, give interpretation and assumption on distribution if any.