Suppose that a manufacturing facility is producing a support beam that is intended to be exactly 10 cm in length, however the beam can be as short as 9.75 cm or as long as 10.5 cm and still fulfill its purpose. Assume that the variation in beam lengths can be modeled as a Normal Distribution, and answer the following questions.

A-Suppose that the average beam produced is slightly too long at 10.1 cm with a standard deviation of 0.4 cm. What is the probability that a bar chosen at random would be 9 cm or less? Round your answer to four decimal points.

B-Suppose instead that the average beam produced has a length of 10.1 cm with a standard deviation of 0.25. What is the probability that a bar chosen at random would be 9.3 cm or more? Express your answer with four decimal points.

C-Suppose that a new version of the product is released which has looser tolerances. Also suppose that management had enough foresight to re-center the manufacturing process to 10 cm and lowered the standard deviation to 0.25 cm. Further suppose that the new tolerances are between 9.5 and 10.25; use P(X<=9.5) = 0.0228 and P(X<=10.25) = 0.8413 to find the percentage of beams that are produced on the new process that meet the new requirements. Round your answer to four decimal points.

D-Suppose instead that the new average for the produced beam is 10.3 cm with a standard deviation of 0.2 and that the new tolerances are from 9.7 cm and 10.7 cm. What is the probability that a bar chosen at random will conform to (be within the) specifications? Express your answer with four decimal points.