2 On average 1 in 4000 people have a particular antigen in their blood (an antigen is a molecule which may cause an adverse reaction).
- A random sample of 1200 people is selected. The random variable \(X\) represents the number of people in the sample who have this antigen in their blood. Explain why you could use either a binomial distribution or a Poisson distribution to model the distribution of \(X\).
- Use either a binomial or a Poisson distribution to calculate each of the following probabilities.
- \(\mathrm { P } ( X = 3 )\)
- \(\mathrm { P } ( X > 3 )\)
- A researcher needs to find 2 people with the antigen. Find the probability that at most 5000 people have to be tested in order to achieve this.