(a) If the absolute measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable and the instrument needs calibration? Round your answer to three decimal places (e.g. 98.765). P = (b) What is the absolute value of measurement error that must be exceeded with probability 0.2 before the instrument needs calibration? Round your answer to three decimal places (e.g. 98.765). a= mm (c) What is the probability that the absolute measurement error is exactly 0.22 millimeters before calibration? P =

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ENGINEERING DATA ANALYSIS

A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration, it is
known that the probability density function of the measurement error is f(x) = 1.0(1-0.5x) for 0 < x < 2.0 millimeters. Note that
x is the absolute value of the measurement error.
(a) If the absolute measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable and
the instrument needs calibration?
Round your answer to three decimal places (e.g. 98.765).
P = i
(b) What is the absolute value of measurement error that must be exceeded with probability 0.2 before the instrument needs
calibration?
Round your answer to three decimal places (e.g. 98.765).
a =
mm
(c) What is the probability that the absolute measurement error is exactly 0.22 millimeters before calibration?
P = i
Transcribed Image Text:A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration, it is known that the probability density function of the measurement error is f(x) = 1.0(1-0.5x) for 0 < x < 2.0 millimeters. Note that x is the absolute value of the measurement error. (a) If the absolute measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable and the instrument needs calibration? Round your answer to three decimal places (e.g. 98.765). P = i (b) What is the absolute value of measurement error that must be exceeded with probability 0.2 before the instrument needs calibration? Round your answer to three decimal places (e.g. 98.765). a = mm (c) What is the probability that the absolute measurement error is exactly 0.22 millimeters before calibration? P = i
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