Question

The average waiting time for getting served at a specific restaurant is 6 minutes. Let X denotes the waiting time to get served at the restaurant, and X follows an exponential distribution. You have waited 2 minutes. What is the probability that you have to wait for another 10 minutes or more to receive your service? report at least two decimal spaces (value between 0 and 1, not in percentage)

Answer 1

Let X be the random variable that denotes the waiting time to get served at the restaurant.

Given, X follows the exponential distribution and the average waiting time for getting served at the restaurant is 6 minutes.

Therefore, X Exponential ( = 1 / 6)

The pdf of X is

f(x) = (1/6) * e^-(1/6)x ; x > 0

      = 0                     ; otherwise

The required probability is

P(X > 12 | X > 2) = P(X > 10)    ..............(by the memoryless property of exponential distribution)

                            = f(x) dx

                            = (1/6) * e^-(1/6)x dx

                            = [-e^-(1/6)x]₁₀

                                  = 0 - (-e^-(1/6)*10)

                            = e^-(1/6)*10

                            = 0.1889

Therefore, the probability that you have to wait for another 10 minutes or more to receive your service is 0.19