The optimal scheduling of preventative maintenance tests of some {but not all} of n independentlyl operating components was developed. The time [in hours) between failures of a componerlt was approximated by an exponentially distributed random variable with mean 9. a. Suppose 3:700 hours. Find the probability that the time between component failures ranges between 1000 and 1500 hours. b. Again, assume 9 = T00 hours. Find the probability that the time between component failures is at least 1000 hours. c. Given that the time between failures is at least 1000 hours, what is the probability that the time between failures is less than 1500 hours? a. The probability that the time between component tailures ranges between 1000 and 1500 hours is 0.1223 _ (Round to tour decimal places as needed.) b. The probability that the time between component failures is at least 1000 hours is; (Round to tour decimal places as needed.)