Metal meter sticks are manufactured on a production line where the true length can be modeled as a normal random variable X with mean 1 m (one meter) and standard deviation 2 mm (two millimeters). (a) Suppose that the meter sticks are checked as they come off the production line and are rejected if they are more than 1 mm short or long. What is the pdf (in units of meters) of the length X of the meter sticks after rejecting those too long or two short? That is, with A = {stick was within tolerance}, find fx|A(x). (b) After the rejection process, what is the probability that the meter stick is within ±0.5 mm of 1 m?

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