Describe, briefly, the conditions under which the binomial distribution Bin(n, p) may be approximated by

(a) a normal distribution,

(b) a Poisson distribution, giving the parameters of each of the approximate distributions. Among the blood cells of a certain animal species, the proportion of cells which are of type A is 0.37 and the proportion of cells which are of type B is 0.004. Find, to three decimal places, the probability that in a random sample of eight blood cells at least two will be of type A. Find, to three decimal places, an approximate value for the probability that

(c) in a random sample of 200 blood cells the combined number of type A and type B cells is 81 or more,

(d) there will be four or more cells of type B in a random sample of 300 blood cells. (L)