The lifetime of a mechanical assembly in a vibration test is exponentially distributedwith a mean of 400 hours.
(a) what is the probability that an assembly on test fails in less than 100 hours?
(b) what is the probability that an assembly operates for more than 500 hours beforefailure?
(c) if an assembly has been on test for 400 hours without a failure, what is theprobability of a failure in the next 100 hours?
(d) if 10 assemblies are tested, what is the probability that at least one fails in lessthan 100 hours? assume that the assemblies fail independently.
(e) if 10 assemblies are tested, what is the probability that all have failed by 800hours? assume the assemblies fail independently.