As study undertaken by the University Hospital of the West Indies (UWHI) found that the number of patients admitted with the COVID-19 virus each day can be modelled by a Poisson distribution with a mean of 2.5 patients being admitted each day
a. i) Calculate p(x=2)
ii) Hence determine the probability that exactly 2 patients will be admitted in three consecutive days .
b. Find the probability that at least 12 patients will be admitted in a one-week period
c. State two assumptions implied by using a Poisson distribution to model the number of patients contracting COVID-19