According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0 < t <∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes.
According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0 < t <∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![According to the U.S. Customs and Border Protection Agency, the average airport wait time (time
from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter-
national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait
time is exponentially distributed so that
p(t) = ke-kt
for 0≤t<∞,
where k is the reciprocal of the average wait time. Assume t is measured in minutes.
1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering
that it is defined for all t≥ 0.)
2. Set up integrals (you can write p(t) for the integrand) for the following probabilities:
(a) Waiting longer than 60 minutes.
(b) Waiting shorter than 30 minutes.
(c) Waiting between 20 and 40 minutes.
3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above)
and convert to a percentage with two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a7e99bb-b9c4-47fa-9081-3b9aeb6b94e4%2Fd80efb0f-9904-42b4-a186-2008f7592119%2F98f0qnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:According to the U.S. Customs and Border Protection Agency, the average airport wait time (time
from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter-
national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait
time is exponentially distributed so that
p(t) = ke-kt
for 0≤t<∞,
where k is the reciprocal of the average wait time. Assume t is measured in minutes.
1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering
that it is defined for all t≥ 0.)
2. Set up integrals (you can write p(t) for the integrand) for the following probabilities:
(a) Waiting longer than 60 minutes.
(b) Waiting shorter than 30 minutes.
(c) Waiting between 20 and 40 minutes.
3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above)
and convert to a percentage with two decimal places.
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