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 1/2 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 1/2 hour. What is the probability that within a 9-hour timeframe, the executive coordinators observe 10 non-overlapping 1/2 hours with at least three delegates each?

d(1-3) The time spent per delegate at the conference can be modelled using a continuous uniform distribution ranging between 1 hour and 5 hours. Considering the arrival of a delegate,

d1 What is the probability that the delegate stays between 90 minutes and 3 hours at the conference?

d2 What is the probability that the delegate stays longer than 4 hours at the conference?

d3 What is the average length of time spent by a delegate at the conference?

Answer 1