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

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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 measurement error within 0.5 millimeters is acceptable, what is the
probability that the error is not acceptable and the instrument needs calibration?
b. What is the value of measurement error that must be exceeded with probability
0.3before the instrument needs calibration?
c. What is the probability that the measurement error is exactly 0.21 millimeters before
calibration?
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 measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable and the instrument needs calibration? b. What is the value of measurement error that must be exceeded with probability 0.3before the instrument needs calibration? c. What is the probability that the measurement error is exactly 0.21 millimeters before calibration?
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