2. In Example 18.3-1, determine the following: (a) The average number of failures per day, assuming the service is offered 24 hours a day, 7 days a week. (b) The probability of at least one failure in a 3-hour period. (c) The probability that the next failure will not occur within 4 hours. (d) If no failure has occurred 3 hours after the last failure, what is the probability that interfailure time is at least 5 hours? ce in with mean Example 18.3-1 A service machine always has a standby unit for immediate replacement upon failure. The time to failure of the machine (or its standby unit) is exponential and occurs every 5 hours, on the average. The machine operator claims that the machine is in the habit" of breaking down every night around 8:30 P.M. Analyze the operator's claim. The average failure rate of the machine is 1 = } = 2 failure per hour. Thus, the exponential distribution of the time to failure is f(1) = 2e-2,1 > 0