The time between arrivals at an ATM machine follows an exponential distribution with θ = 10 minutes. Find the probability that between 15 and 25 minutes will pass between arrivals.
A) 0.223130
B) 0.082085
C) 0.141045
D) 0.305215

Question

Quizplus · Accepted Answer

The exponential distribution with parameter θ = 10 has a probability density function f(x) = (1/θ) * e^(-x/θ). The probability that the time between arrivals is between 15 and 25 minutes is given by the integral of the density function from 15 to 25, which is F(25) - F(15) = (1 - e^(-25/10)) - (1 - e^(-15/10)) = e^(-15/10) - e^(-25/10) = 0.141045.

The Time Between Arrivals at an ATM Machine Follows an Exponential