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

Question

Quizplus · Accepted Answer

The exponential distribution with parameter $\theta = 10$ has a probability density function $f(x) = \frac{1}{\theta} e^{-x/\theta}$. The probability that more than 25 minutes will pass is given by $P(X > 25) = e^{-25/10} = e^{-2.5} \approx 0.082085$.

The Time Between Arrivals at an ATM Machine Follows an Exponential