The U. S. Army commissioned a study to assess how deeply a bullet penetrates ceramic body armor. In the standard test, a cylindrical clay model is layered under the armor vest. A projectile is then fired, causing an indentation in the clay. The deepest impression in the clay is measured (in mm) as an indication of the survivability of someone wearing the armor. Out of 20 different samples of the body armor, the average indentation in the clay was ¯x = 33.370 mm with standard deviation s = 5.268 mm. (a) Calculate and interpret a 95% upper confidence bound for the true average indentation depth. What, if any, assumptions did you make in order to compute this interval, and why did you need to make them? (b) Calculate and interpret a 95% confidence interval for the true average indentation depth, under the same assumptions you used in part (a). (c) Calculate and interpret a 95% prediction interval for the indentation depth of the next piece of body armor produced, under the same assumptions you used in previous parts.