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?
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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![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc012e98d-11f3-4ebf-9e91-31a87ace6c91%2Fb5f993e1-40d2-42d2-8e0f-1d7be9b29512%2Fywxwhcs_processed.png&w=3840&q=75)
Transcribed Image Text: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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