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 0.3 before the instrument needs calibration? c. What is the probability that the measurement error is exactly 0.21 millimeters before calibration?
A test instrument needs to be calibrated periodically to prevent measurement errors. After some time of use without calibration, it is known that the
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 0.3 before the instrument needs calibration?
c. What is the probability that the measurement error is exactly 0.21 millimeters before calibration?
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