Amanufacturer produces crankshafts for an automobile engine. the wear of the crankshaft after 100,000 miles (0.0001 inch) is of interest because it is likely to have an impact on warranty claims. a random sample of n = 15 shafts is tested and x - = 2.78. it is known that sigma = 0.9 and that wear is normally distributed. a. test h0: mu = 3 versus ? 1: mu 3 using alpha = 0.05. b. what is the power of this test if mu, = 3.25? c. what sample size would be required to detect a true mean of 3.75 if we wanted the power to be at least 0.9?

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.