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The time between arrivals of taxis at a busy intersection
Chapter 4, Problem 121E(choose chapter or problem)
Problem 121E
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.
(a) What is the probability that you wait longer than one hour for a taxi?
(b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes?
(c) Determine x such that the probability that you wait more than x minutes is 0.10.
(d) Determine x such that the probability that you wait less than x minutes is 0.90.
(e) Determine x such that the probability that you wait less than x minutes is 0.50.
Questions & Answers
QUESTION:
Problem 121E
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.
(a) What is the probability that you wait longer than one hour for a taxi?
(b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes?
(c) Determine x such that the probability that you wait more than x minutes is 0.10.
(d) Determine x such that the probability that you wait less than x minutes is 0.90.
(e) Determine x such that the probability that you wait less than x minutes is 0.50.
ANSWER:
Solution
Step 1 of 5
Let X be the time between the arrivals of taxi
Here X is exponential random variable with mean of 10 min
Then
a) We have to find the probability that you wait longer than one hour for taxi
Here one hour=60 minutes
The cumulative density function of exponential distribution is
We have to find
=
=
=0.0025
Hence the probability that you wait longer than one hour for taxi is 0.0025