Answer :
The length of an interval of time such that the probability that no messages arrive during this interval is 0.94 is 56.88 seconds.
We have to find the length of the time interval that the probability of no messages arrive during this interval is 0.94
Let X be the no.of messages arrive to the server
X follows the poisson distribution with mean λ = 17
Let t be the time interval
The probability of no messages arrive during this interval is 0.94
Then P(0) = 0.94
e⁻⁽λt⁾ = 0.94
λt = ln0.94
17 t = ln(0.94)
t = ln(0.94)/17
t = 0.026872 / 17 hrs
t = 0.0158
Convert 0.0158 hours to seconds
That is t=0.0158(60)(60)
=56.88seconds
Hence in 56.88 seconds the time interval that the probability of no messages arrive during this interval is 0.94 .
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