An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 2000 mm and a standard deviation of 80 mm. A) Find the 68th percentile, P68, which is the length that separates the bottom 68% lengths of subcomponents from the top 32%. Such a percentile is P68 = (Round your answer to 2 decimal places).

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An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 2000 mm and a standard deviation of 80 mm.

A) Find the 68th percentile, P68, which is the length that separates the bottom 68% lengths of subcomponents from the top 32%.
Such a percentile is P68 =
(Round your answer to 2 decimal places).


B) What is the probability that a randomly chosen subcomponent has length greater than 2008 mm?
(Round your answer to 4 decimal places).


C) What is the probability that 16 randomly selected subcomponents have a mean length greater than 2008 mm? Use the Central Limit Theorem to answer this question.
(Round your answer to 4 decimal places).

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