Sp07_Final-Posted

# Sp07_Final-Posted - Name FINAL EXAMINATION STAT 427 1[25...

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Name_______________________________ 1 of 4 5/31/2011 FINAL EXAMINATION - STAT 427 1. [25 points] During slack periods, trucks arrive independently at a weighing station at an average rate of 10 per hour. Suppose that with probability 0.95 an arriving truck will have no overweight violations. a) [5 points] What is the distribution of total time between any four consecutive trucks entering the inspection station? b) [8 points] Find the probability that two or more trucks enter the station during a randomly selected 15-minute period and none of these have overweight violations. c) [4 points] Less than one vehicle entering the station in any 15-minute period leads to the early closure of the station at the end of the period. The station is monitored during 40 independent 15-minute periods over various days. Let Y denote the number of times that the station is closed for the day among these 40 trials. What is the distribution of Y? d) [8 points] The slack duration of 10 hours in a day is divided into 40 consecutive non- overlapping 15-minute periods. Less than one vehicle entering the station in a period leads to the early closure of the station for the day. If the station doesn’t close early, it closes for the day automatically at the end of the 10 hour period. For 1,2, ,40 i , th 1, if the station is closed in the i period, 0, otherwise.

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Sp07_Final-Posted - Name FINAL EXAMINATION STAT 427 1[25...

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