2.2.19 Consider a manufacturing process that is producing hypodermic needles that will be used for d) blood donations. These needles need to have a diameter of 1.65 mm - too big and they would hurt the donor (even more than usual), 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 signicant 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. Identify the variable of interest, and whether the variable is categorical or quantitative. Write the appropriate hypotheses using appropriate symbols, to test whether the average diameter of needles from the manufacturing process is different from the desired value. Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm, and a standard deviation of 0.07mm. Assign appropriate symbols to these numbers. Suppose that the diameters of needles produced by this manufacturing process have a bellshaped distribution. Sketch the distribution of the average diameter of samples of 35 needles, assuming