Imagine that we are studying an area with bee hives and we have been told that the mean number of bee hives per acre is 4. Bee hives are founded by queens that disperse by flight from their natal nests so we will assume that their locations are randomly based on where the female landed. (provide all values to the nearest 0.0001 and be cautious about rounding error)

a) If we randomly choose an acre to search for bee hives, what is the probability that we find exactly three?

b)If we randomly choose an acre to search for bee hives, what is the probability that we find more than three?

(c)If we randomly choose an acre to search for bee hives, what is the probability that we find four or five?

(d) If we sampled a large number of random acres to search for bee hives, what proportion of them will yield more than six hives?

(e,) If we sampled two acres, what is the probability that we find exactly six in both?