Question

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.