In the past decade, two presidential elections in the United States have witnessed very long wait times at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Philadelphia as well, some voters complained about the long lines in some precincts, with most complaints coming from precinct A. In 2004, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1). Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine), with a standard deviation of 120 seconds. Q3. Under Proposal 1, at precinct A, what would be the ratio of the average number of people voting (at a booth) over the average number of people in the line (waiting)? Please show and explain this problem.
In the past decade, two presidential elections in the United States have witnessed
very long wait times at precincts (voting stations) in states that ultimately decided
the election (Florida in 2000 and Ohio in 2004).
In Philadelphia as well, some voters complained about the long lines in some
precincts, with most complaints coming from precinct A. In 2004, the average
number of voters arriving at Precinct A was 35 per hour and the arrivals of voters
was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1).
Philadelphia deployed 1 voting machine in Precinct A. Suppose that each voter
spent on average 100 seconds in the voting booth (this is the time needed to cast
her/his vote using a voting machine), with a standard deviation of 120 seconds.
Q3. Under Proposal 1, at precinct A, what would be the ratio of the average number
of people voting (at a booth) over the average number of people in the line
(waiting)?
Please show and explain this problem.
Since the arrivals of voters are random, we can assume that they follow a Poisson process. The mean inter-arrival time is given by 1/λ, where λ is the arrival rate. In this case, the arrival rate is 35 per hour, so the mean inter-arrival time is 1/35 hours = 102.86 seconds.
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