A sample of students that had stuffy or runny noses were blindly given a single Skittles candy to put in their mouth. They were told the five possible flavors and then were asked which flavor they had. Of the 100 students tested, 40 gave the correct answer. (3 pts) Can we use theory-based approach for calculating the confidence interval? Explain. Yes because (4 pts) Find a 95% confidence interval for the proportion of all students with stuffy or runny noses that could correctly identify a Skittles flavor blindly. Show all your work. Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mmtoo big and they would hurt the donor, too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. Suppose the most recent random sample of 35 needles