The number of ﬂoods that occur in a certain region over a given year is a...

The number of ﬂoods that occur in a certain region over a given year is a random variable having a Poisson distribution with mean 2, independently from one year to the other. Moreover, the time period (in days) during which the ground is ﬂooded, at the time of an arbitrary ﬂood, is an exponential random variable with mean 5. We assume that the durations of the ﬂoods are independent. Using the 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 do not need to apply half-unit correction for this question.

(b) the probability that the total time during which the ground will be ﬂooded over the course of the next 50 ﬂoods will be smaller than 200 days.

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milcah answered 9 months ago

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