A viral infection is spread by contact with an infected person. Suppose that an infected person has contact with 15 healthy people, let X denote the number of people (out of these 15) who are...

Extracted text: A viral infection is spread by contact with an infected person. Suppose that an infected person has contact with 15 healthy people, let X denote the number of people (out of these 15) who are infected. By “infected" we mean that the person develops symptoms of the infection. Based on previous research, the infection rate is 25%. After how many positive cases can we conclude the infection rate is acutally higher than 25%? (What is the lowest number of positive cases?)