4. (a) Write down two conditions needed to be able to approximate the binomial distribution by the Poisson distribution. A researcher has suggested that 1 in 150 people is likely to catch a particular virus.
Assuming that a person catching the virus is independent of any other person catching it,
(b) find the probability that in a random sample of 12 people, exactly 2 of them catch the virus.
(c) Estimate the probability that in a random sample of 1200 people fewer than 7 catch the virus.