Question

please use Poisson Processes to answer the below question :

Q. Voters arrive at a polling booth in a remote Queensland town at an average rate of 30

per hour. There are two candidates contesting the election and the town is divided. Candidate

A is far more popular, and is known that any voter will vote for her with probability 0.85.

(a) The electoral officer arrived exactly 6 minutes late to open the booth, and one voter was

waiting outside. What is the probability that the voter had been waiting for more than 5

minutes? You may assume that they did not arrive before the polling booth was meant to

open.

(b) Due to social distancing measures, voters that arrive within a minute of another voter must

wait outside. What is the probability that, when you turn up to vote, you need to wait

outside?

(c) What is the expected number of votes that Candidate A will receive during the 8 hour

voting period?

(d) By the time the election has closed, exactly 8 hours after it started, exactly 238 voters had

cast their vote and Candidate A had won 198 votes to 40. Use a normal approximation

to compute the probability that the candidate A had received enough votes to win in the

first 4 hours of the election. Ensure you validate the assumptions required to use a normal

approximation and apply a continuity correction.

Answer 1

Answer:

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