In: Statistics and Probability
Suppose that at the beginning of March, a new strain of flu, flu-A, emerges and begins to spread through U-College undergraduates. The symptoms of Flu-A are like the common flu, flu-B, and other respiratory illnesses. It is thought that the infection rate of Flu-A will be similar to that of Flu-A at other colleges, but that the disease will be much less deadly. Flu-A is expected to infect about 20 out of every 1,000 undergraduate students per month for the rest of the semester, while the flu-B is expected to infect about 30 out of every 1,000 undergraduates per month for the rest of the semester. Assume that this rate remains the same for each of the remaining months in the semester (March, April, and May). There are currently 6,800 U-College undergraduates on campus. You may assume that infection with Flu-A is independent of infection with the flu-B.
1. Calculate the total expected number of Flu-A cases among U College undergraduates over the next three months.
2. If more than 150 cases of Flu-A are observed among the undergraduates during the next month, the College will go into shut-down mode and cancel class meetings. What is the probability the College goes into shut-down mode by the end of March?