The waiting time (in minutes)between ordering and receiving your meal at a certain restaurant is exponentially distributed with a mean of 10 minutes. The restaurant has a policy that your meal is
Free if you have to wait more than 25 minutes after ordering. What is the probability of receiving a
Free meal?
A)0.329680
B)0.917915
C)0.082085
D)0.670320

Question

Quizplus · Accepted Answer

The waiting time being exponentially distributed with a mean of 10 minutes means the rate parameter $ \lambda = \frac{1}{10} $. The probability of waiting more than 25 minutes is $ P(T > 25) = e^{-\lambda t} = e^{-\frac{25}{10}} = e^{-2.5} \approx 0.082085 $.

The Waiting Time (In Minutes)between Ordering and Receiving Your Meal