- State Two Conditions Under Which A Binomial Distribution May Be Approximated By A Poisson Distribution And Give A Reaso 1 (114.43 KiB) Viewed 33 times
step involving in the solution.
State two conditions under which a binomial distribution may be approximated by a Poisson distribution, and give a reason why this approximation may be useful in practice. In the treatment of hay fever, the probability that any sufferer is allergic to a particular drug is 0.0005. Assuming that the occurrences of the allergy in different sufferers are independent, find the probability that in a random sample of 8000 sufferers more than four will be allergic to the drug. Each sufferer who is allergic to the drug has a probability of 0.3 of developing serious complications following its administration. (a) Determine the probability that, of the 8000 sufferers who are administered the drug, exactly two develop serious complications. In fact four sufferers develop the allergy following the administration of the drug to the random sample of 8000 sufferers. (b) Determine the probability that exactly two of these four develop serious complications. Explain, briefly, why your answers to (a) and (b) differ. (AEB)