(Solution) - In an automatic geo location system a dispatcher sends a message -(2025 Original AI-Free Solution)

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In an automatic geo-location system, a dispatcher sends a message to six trucks in a fleet asking their locations. The waiting times for responses from the six trucks are iid exponential random variables, each with expected value 2 seconds.
(a) What is the probability that all six responses will arrive within 5 seconds?
(b) If the system has to locate all six vehicles within 3 seconds, it has to reduce the expected response time of each vehicle. What is the maximum expected response time that will produce a location time for all six vehicles of 3 seconds or less with probability of at least 0.9?