If arrivals occur at a mean rate of 1.6 events per minute, the exponential probability of waiting less than 1 minute for the next arrival is:
A).2019.
B).7104.
C).8812.
D).7981.

Question

Quizplus · Accepted Answer

The exponential probability of waiting less than a certain time $ t $ for the next arrival when events occur at a mean rate $ \lambda $ per unit time is given by $ 1 - e^{-\lambda t} $. Here, $ \lambda = 1.6 $ events per minute and $ t = 1 $ minute. Thus, the probability is $ 1 - e^{-1.6 \times 1} = 1 - e^{-1.6} $. Calculating this gives approximately 0.7981, or 79.81% when expressed as a percentage. Therefore, the correct choice is D, which corresponds to 7981 in the format provided by the options.

If Arrivals Occur at a Mean Rate of 1