The average time between phone calls arriving at a call centre is 30 seconds.Assuming that the time between calls is exponentially distributed, find the probability that less than two minutes elapse between calls.
A)0.018
B)0.064
C)0.936
D)0.982
E)1.000

Question

Quizplus · Accepted Answer

The probability that less than two minutes elapse between calls is the integral of the exponential distribution from 0 to 120 seconds. The exponential distribution is given by f(x) = lambda * e^(-lambda * x), where lambda is the average time between calls. In this case, lambda = 1/30 = 0.0333. So, the probability is:P(X < 120) = integral from 0 to 120 of 0.0333 * e^(-0.0333 * x) dx = 0.982

The Average Time Between Phone Calls Arriving at a Call