Due to the complexities of car engines, parts must be manufactured to exact size or will not function properly. Evan's facility manufactures a universal piston which should work with various engines, and therefore various makes and models of cars. The diameter of this universal piston is known to have a distribution that is mound-shaped and symmetric with a mean of 2.75 inches and a standard deviation of 0.07 inches. a) Toyota has an engine which requires its pistons to be between 2.61 and 2.82 inches. Determine the proportion of pistons from Evan's facility that will meet this requirement. b) Ford has an engine that requires a maximum piston diameter of 2.96 inches. Determine the proportion of pistons from Evan's facility that will not meet this requirement.
