1 A study undertaken by Goodhealth Hospital found that the number of patients each month, \(X\), contracting a particular superbug can be modelled by a Poisson distribution with a mean of 1.5 .
- Calculate \(\mathrm { P } ( X = 2 )\).
- Hence determine the probability that exactly 2 patients will contract this superbug in each of three consecutive months.
- Write down the distribution of \(Y\), the number of patients contracting this superbug in a given 6-month period.
- Find the probability that at least 12 patients will contract this superbug during a given 6-month period.
- State two assumptions implied by the use of a Poisson model for the number of patients contracting this superbug.