Traffic data are collected in 60-second intervals at a specific highway location as shown in the Table. Assuming the traffic arrivals are Poisson distributed and continue at the same rate as that observed in the 15 time periods shown, what is the probability that six or more vehicles will arrive in each of the next three 60-second time intervals (12:15 P.M. to 12:16 P.M., 12:16 P.M. to 12:17 P.M., and 12:17 P.M. to 12:18 P.M.)?

Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter9: Capacity And Level Of Service For Highway Segments
Section: Chapter Questions
Problem 18P
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Traffic data are collected in 60-second intervals at a specific highway location as shown in the Table. Assuming the traffic arrivals are Poisson distributed and continue at the same rate as that observed in the 15 time periods shown, what is the probability that six or more vehicles will arrive in each of the next three 60-second time intervals (12:15 P.M. to 12:16 P.M., 12:16 P.M. to 12:17 P.M., and 12:17 P.M. to 12:18 P.M.)?

Time period
Observed number of vehicles
12:00 P.M. to 12:01 P.M. 3
12:01 P.M. to 12:02 P.M. 5
12:02 P.M. to 12:03 P.M. 4
12:03 P.M. to 12:04 P.M. 8
12:04 P.M. to 12:05 P.M. 7
12:05 P.M. to 12:06 P.M. 4
12:06 P.M. to 12:07 P.M. 8
12:07 P.M. to 12:08 P.M. 5
12:08 P.M. to 12:09 P.M. 9
12:09 P.M. to 12:10 P.M. 5
12:10 P.M. to 12:11 P.M. 3
12:11 P.M. to 12:12 P.M. 10
12:12 P.M. to 12:13 P.M. 9
12:13 P.M. to 12:14 P.M. 7
12:14 P.M. to 12:15 P.M. 6
Transcribed Image Text:Time period Observed number of vehicles 12:00 P.M. to 12:01 P.M. 3 12:01 P.M. to 12:02 P.M. 5 12:02 P.M. to 12:03 P.M. 4 12:03 P.M. to 12:04 P.M. 8 12:04 P.M. to 12:05 P.M. 7 12:05 P.M. to 12:06 P.M. 4 12:06 P.M. to 12:07 P.M. 8 12:07 P.M. to 12:08 P.M. 5 12:08 P.M. to 12:09 P.M. 9 12:09 P.M. to 12:10 P.M. 5 12:10 P.M. to 12:11 P.M. 3 12:11 P.M. to 12:12 P.M. 10 12:12 P.M. to 12:13 P.M. 9 12:13 P.M. to 12:14 P.M. 7 12:14 P.M. to 12:15 P.M. 6
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