Solve the problem.
-The length of time for telephone conversations (in minutes) is exponentially distributed. The average (mean) length of a conversation is 5 minutes. What is the probability that a conversation lasts less than 3 minutes?
A) 0.189
B) 0.451
C) 0.549
D) 0.811

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $ P(X < x) = 1 - e^{-\lambda x} $, where $ \lambda = \frac{1}{\text{mean}} $. Given the mean is 5 minutes, $ \lambda = \frac{1}{5} $. For $ x = 3 $ minutes, $ P(X < 3) = 1 - e^{-\frac{1}{5} \cdot 3} = 1 - e^{-0.6} \approx 0.451 $.

Solve the Problem. -The Length of Time for Telephone Conversations (In Minutes) Is