The time between arrivals at an ATM machine follows an exponential distribution with θ = 10 minutes. Find the probability that less than 25 minutes will pass between arrivals.
A)0.917915
B)0.329680
C)0.670320
D)0.082085

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\frac{x}{\theta}}$, where $\theta$ is the mean time between arrivals. Plugging in the values, we get $P(X < 25) = 1 - e^{-\frac{25}{10}} = 1 - e^{-2.5} \approx 0.917915$.

The Time Between Arrivals at an ATM Machine Follows an Exponential