Question

It is known that the waiting time for a car to pass by on a country road is exponentially distributed with an average wait time of 19 minutes. Given that it has already taken 20 minutes, what is the probability that the wait time will be more than an additional 23 minutes? Round your answer to three decimal places.

Answer 1

0.298

Explanation:

in this case we have an exponential distribution:

1 - e ^ (- x / y)

where x and y corresponds to the times we find in the exercise.

Now follows memoryless property.

P (More than 23 additional minutes | 20 minutes passed)

P = P (More than 23 minutes)

P = 1 - P (Less than or equal to 23 minutes)

P = 1 - (1 - e ^ (- 23/19))

P = 0.298

Therefore the probability is 29.8%