Answer:
0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes
Step-by-step explanation:
To solve this question, we need to understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: It has already taken 11 minutes.
Event B: It will take 16 more minutes.
Exponentially distributed with an average wait time of 14 minutes.
This means that
Probability of the waiting time being of at least 11 minutes:
Probability of the waiting time being of at least 11 minutes, and more than an additional 16 minutes:
More than 11 + 16 = 27 minutes. So
What is the probability that the wait time will be more than an additional 16 minutes?
0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes