A certain type of lobster is exceedingly rare; roughly 1 in every 35 million lobsters hatched is this type of lobster. Apply the Poisson approximation to the binomial distribution to answer the following questions. a. Of 100 million lobsters hatched, what is the probability that between 3 and 5, inclusive, are this type of lobster? b. Roughly how many lobsters must be hatched in order to be at least 80% sure that at least one is this type of lobster? a. The probability that there are between 3 and 5 rare lobsters of this type in a random sample of 100 million is approximately . (Round to four decimal places as needed.)