Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80%80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5%5% of vaccinated children. A group of 2020 children at a nursery school is exposed to whooping cough by playing with an infected child.
(a) If all 2020 have been vaccinated, what is the mean number of new infections? (Enter your answer as a whole number.)
mean number of new infections =
(b) If none of the 2020 have been vaccinated, what is the mean number of new infections? (Enter your answer as a whole number.)
mean number of new infections =
(c) What is the probability that 1818 or more of the 2020 children develop infections? (Enter your answer rounded to four decimal places.)