Dragon boat racing is a competitive water sport that involves 20 paddlers propelling a boat across various race distances. A study on elite dragon boat paddlers summarized an extensive statistical analysis of data obtained from a sample of 11 paddlers. It reported that a 95% confidence interval for true average force (N) during a simulated 200-m race was [60.2, 70.6]. Assume the paddling force is normally distributed. (a) Briefly describe what needs to be done in order to assume "the force is normally distributed".
(b) Obtain a 95% prediction interval for the force of a single randomly selected dragon boat paddler undergoing the simulated race.
(c) Calculate an interval that includes at least 99% of the paddling forces in the popula- tion distribution using a confidence level of 95%.
(d) Calculate a two-sided 99% confidence interval for the population variance of paddling force in the simulated race.
(e) Calculate an upper confidence bound with confidence level 95 % for the population.