A factory produces metal bars used in the steering columns of cars. The car manufacturer requires that the bars are 60 ± 0.15 cm in length. The lengths of bars produced are normally distributed with a...

A factory produces metal bars used in the steering columns of cars. The car manufacturer
requires that the bars are 60 ± 0.15 cm in length. The lengths of bars produced are
normally distributed with a mean of 60.03 cm and a standard deviation of 0.08 cm.
(a) Calculate the proportion of metal bars with lengths exceeding 60.15 cm.
(b) What percentage of bars produced by the factory is acceptable to the car
manufacturer?
(c) Find the bar length, correct to two decimal places, such that 10% of bars are
shorter than this value.