If arrivals follow a Poisson distribution with mean 1.2 arrivals per minute, find the 75^th percentile of waiting times until the next arrival (i.e., 75 percent below). A)1.155 minutes (69.3 seconds) B)0.240 minute (14.4 seconds) C)1.919 minutes (115.1 seconds)

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Quizplus · Accepted Answer

The 75th percentile of waiting times in a Poisson distribution can be found using the exponential distribution formula: $T = \frac{-\ln(1-p)}{\lambda}$, where $p$ is the percentile in decimal form (0.75 for the 75th percentile) and $\lambda$ is the rate of arrivals per unit time (1.2 arrivals per minute). Plugging in the values gives $T = \frac{-\ln(1-0.75)}{1.2} \approx 1.155$ minutes, which is choice A.

If Arrivals Follow a Poisson Distribution with Mean 1