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− 0.5x for 0 < x < 2 millimeters.

(a) If the measurement error within 0.5 millimeters is acceptable, what is the probability that the error is not acceptable before calibration?

(b) What is the value of measurement error exceeded with probability 0.2 before calibration?

(c) What is the probability that the measurement error is exactly 0.22 millimeters before calibration?