Question

If the time between calls in a call center follows an Exponential Distribution with mean 5 minutes, what is the probability that there will not be another call in the next 10 minutes?

Answer 1

For the exponential distribution, the mean is

$5 = E[X] = 1/\lambda \; \Longrightarrow\; \lambda = 1/5$

'will not be another call in the next 10 minutes' = 'the next call will be after 10 min'

$P(X>10) =1 - P(X \leq 10) = 1-(1 -e ^{-10 \lambda}) = 1-(1 -e ^{-10/5})= 1-(1 -e ^{-2})= 1 -1 + 0.1353 = 0.1353$

Answer: 0.1353