題組內容

2. An outbreak of acute gastroenteritis occurred at a nursing home in Baltimore, Maryland, in December 1980. A total of 46 out of 98 residents of the nursing home became ill. People living in the nursing home shared rooms: 13 rooms contained 2 occupants, 4 rooms contained 3 occupants, and 15 rooms contained 4 occupants. One question that arises is whether or not a geographical clustering of disease occurred for persons living in the same room. A summary of the number of affected people and the total number of people in a room is given in Table 2.

b. (10%) One useful summary measure of geographical clustering is the number of rooms with 2 or more affected occupants. If the binomial distribution holds, what is the expected number of rooms with 2 or more affected occupants over the entire nursing home?