A radio manufacturer uses four different resistors as part of a tuner system. The resistor manufacturer specifies that each resistor has a lifetime modeled adequately by a Weibull distribution with shape parameter 2.0. The four resistors have characteristic lives, in hours of average radio usage, of 1000, 1200, 1500, and 2000 hours, respectively. What is the life distribution for time to first resistor failure? What is the radio MTTF? (Hint: I = 0.88623.) What is the median failure time for the radio? How likely is it that no resistor fails in the first 168 hours? In the first 1000 hours?