The number of voters arriving at a polling station follows a Poisson distribution with 5 voters in 20 minutes. Calculate the probability that no voter will arrive between 3:10 and 3:30 pm.

Here are the solutions to the questions: 4. (i) The number of voters arriving at a polling station follows a Poisson distribution with 5 voters in 20 minutes. This means the average rate for a 20-minute interval is 5. The probability mass function for a Poisson distribution is P(X=x) = e^- ^xx!. a) Calculate the probability that no voter will arrive between 3:10 and 3:30 pm. The time interval is 3:30 - 3:10 = 20 minutes. For this interval, = 5. We need to find P(X=0).