At the Christina Steel Company (CSC), steel rods are manufactures with a mean length of 25 centimeter (cm). Because of variability in the manufacturing process, the length of the rods are approximately normally distributed, with a standard deviation of 0.08 centimeter. Please show all calculations and drawing...

a. What is the probability that a randomly selected rod has a length longer than 26.03 cm? (4 points)

b. What is the probability that a randomly selected rod has a length shorter than 24 cm?

c. Any rods not between the lengths of 24.85 cm and 25. 08cm will be discarded. What is the probability that a randomly selected rod will be discarded?

d. Trudy Manufacturing Inc. (TM), just informed CSC that they will only order rods within the middle 85% of all rods. You, as the Product Analyst at TM, are tasked to determine the acceptable lengths of these rods. (4 points) e. DeRosa Mining Company (DMC), another client of CSC, just informed them that they will only seek to order rods within the top 11 %. What is the cutoff length?