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 $\lambda$ for a 20-minute interval is 5. The probability mass function for a Poisson distribution is $P(X=x) = \frac{e^{-\lambda} \lambda^x}{x!}$.

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, $\lambda = 5$. We need to find $P(X=0)$.