Problem 1) 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)