Volcanic eruptions of Mt. Vesuvius follow a Poisson distribution with an average of 2.5 eruptions every 100 years. Use that to answer the following:
a) Find the probability that there will be exactly 3 eruptions in the next 200 years. (6 points) (Round your answer to 4 decimal places)
b) Find the probability the next eruption occurs between 25 and 50 years. (6 points) (Round your answer to 4 decimal places)
