Question

If the interarrival time is exponential and 8 customers per hour arrive in a bank, then the probability of no arrival of customer during a period of 15 minutes is \(\underline{\hspace{2cm}}\). [round off to two decimal places]

Hint:

For exponential interarrival times (Poisson arrivals), $P(0)=e^{-\lambda t}$ gives the probability of no arrivals in a time interval.

Answer 1

Correct Answer: 0.12 - 0.15

Arrival rate: \[ \lambda = 8\ \text{customers/hour} \] Time interval: \[ 15\ \text{min} = 0.25\ \text{hour} \] For a Poisson process, probability of zero arrivals: \[ P(0) = e^{-\lambda t} \] Substitute: \[ P(0) = e^{-8(0.25)} = e^{-2} \] \[ P(0) \approx 0.1353 \] Thus, the probability lies in the range: \[ \boxed{0.12\text{ to }0.15} \]