Solution
The Quiet Line
Show the problem again
Calls arrive at a help desk according to a Poisson process with rate 6 calls per hour. What is the probability that no call arrives during a given 10-minute interval? Give an exact expression or a decimal rounded to 3 decimal places.
Worked solution
The answer is 1/e ≈ 0.368. The number of calls in a 10-minute window is Poisson with mean 6 × (1/6) = 1, so the probability of zero calls is e^(−1). Equivalently, the waiting time for the next call is exponential with mean 10 minutes, and P(wait > 10) = e^(−1).
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.