Question

The number of delegates that arrives at a day-long business conference during a major snowstorm follows a poisson process with a rate of 2 delegates every 10 minutes.

a) Solve for the probability that at least three delegates arrive at the conference in the next half hour?

b) Suppose the conference runs from 9 am to 6 pm, what is the expected # of delegates that will arrive during that timeframe? What is the variance of the expected # of delegates that will arrive during that timeframe?

c) Considering the 9-hour timeframe, the executive coordinators want to track the busiest time(s) of the day, and thus decide to record the # of delegates arriving at the conference every half hour. What is the probability that within a 9-hour timeframe, the executive coordinators observe 10 non-overlapping half hours with at least three delegates each?

*Please don't copy other experts' solution.

Answer 1