A certain type of lobster is exceedinglyrare; roughly1in every30million lobsters hatched is this type of lobster. Apply the Poisson approximation to the binomial distribution to answer the following questions.a. Of200million lobstershatched, what is the probability that between4and6,inclusive, are this type oflobster?b. Roughly how many lobsters must be hatched in order to be at least95%sure that at least one is this type oflobster?

a. The probability that there are between4and6rare lobsters of this type in a random sample of200million is approximately______.

(Round to four decimal places asneeded.)

b. In order to be at least95%sure that there is at least one of this type of lobster in thesample, there must be at least_____lobsters in the sample.

(Do not round until the final answer. Then round up to the nearestinteger.)