In the previous two presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Washington DC 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 of 35 per hour and the arrivals of voters followed a Poisson process (which is a common arrival pattern). DC had 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.

2a. How long on average a voter had to wait in line precinct at A in 2004 beforeentering in a booth where the machine is to cast her/his vote. Circle the closest answer.

a. 56 minutes

b. 58 minutes

c. 60 minutes

d. 62 minutes

e. 71 minutes

f. 75 minutes

g. There is not sufficient information to answer the question

Given the long wait times for Precinct A, DC is thinking of alternative solutions to improve voting conditions. One of the proposed solutions is as follows.?

Proposal 1: Deploy an additional voting machine in precinct A.?

Assume that the voter turnout is expected to have similar characteristics in 2008 as in the previous election.

2b. Under Proposal 1, how long on average would a voter have to wait in line in precinct A in 2008 before casting her/his vote. Circle the closest answer.

a. 1 minute

b. 5 minutes

c. 6 minutes

d. 10 minutes

e. 11 minutes

f. There is not sufficient information to answer the question

2c. Under Proposal 1, on average, 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)

a. 0.4

b. 1.4

c. 2.4

d. 3.4

e. 4.4

f. 5.4

g. There is not sufficient information to answer the question

My-law.com Legal Services

My-law.com is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply to lazy for entering a law office. Unlike traditional law firms, My-law.com allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship.

In order to allow customers to interact with the firm's lawyers, customers are encouraged to send emails to [email protected]. From there, the incoming emails are distributed to the lawyer who is currently "on call". Given the broad skills of the lawyers, each lawyer can respond to each incoming request.

Emails arrive from 8am to 6pm at a rate of 10 emails per hour (coefficient or variation for the arrivals is 1). At each moment in time, there is exactly one lawyer "on call", i.e. sitting at his/her desk, waiting for incoming emails. It takes the lawyer, on average, 5 minutes to write the response email. The standard deviation of this is 4 minutes.

1.While not responding to emails, the lawyer on call is encouraged to actively pursue cases that potentially could lead to large settlements. How much time over a 10h day can a my-law.com lawyer dedicate to this activity? Assume the lawyer can instantly switch between emails and work on a settlement.(Hint: The lawyer is working on a settlement when he is not responding to emails, i.e., he is idle from the email answering "queue").

a. 600 minutes

b. 120 minutes

c. 100 minutes

d. 80 minutes

e. None of the above

To increase the responsiveness of the firm, the board of my-law.com proposes a new operating policy. Under the new policy, the response would be highly standardized, reducing the standard deviation for writing the response email to 0.5 minutes. The average writing time would remain unchanged.

2How would the amount of time a lawyer can dedicate to the search for large settlement cases change with this new operating policy?

a.It would go up

b.It would go down

c.It would remain unchanged

d.Can not be determined as it depends on the variability

3.Now, what is the average time a customer has to wait for the response to her email? (Circle the closest answer)

a. 5.1 minutes

b. 10.2 minutes

c. 12.6 minutes

d. 14.1 minutes

e. 17.6 minutes

Answered all the questions with explaination in solution file