In the 1990s in the US, oil spill events of over 10,000 gallons occur at a rate of approximately 12 per month. Assume such occurrences during each time period follow a Poisson distribution with λ proportional to the length of time.
(a) During a particular month, what is the probability that there is exactly one oil spill event of over 10,000 gallons?
(b) Would you be surprised if there were more than 5 events of over 10,000 gallons during a particular week? Assume a month = four weeks and calculate the probability.
(c) What is the standard deviation of the number of oil spills of over 10,000 gallons during a 4 month period?