The number of floods that occur in a certain region over a givenyear is a random variable having a Poisson distribution with mean2, independently from one year to the other. Moreover, the timeperiod (in days) during which the ground is flooded, at the time ofan arbitrary flood, is an exponential random variable with mean 5.We assume that the durations of the floods are independent. Usingthe central limit theorem, calculate (approximately)
(a) the probability that over the course of the next 50 years,there will be at least 80 floods in this region. Assume that we donot need to apply half-unit correction for this question.
(b) the probability that the total time during which the groundwill be flooded over the course of the next 50 floods will be smallerthan 200 days.
