At a certain university, a large course has 1500 registered students; the course can be viewed online if a student does not feel like walking to the lecture hall. Each student decides each day (independently of the other students and independent of her/his own prior behavior) whether to attend the class in the lecture hall or just view the online version. The probability a student attends class in the lecture hall is only 0.30J so the registrar has quite a headache.
a. What is the expected number of students to attend class in the lecture hall on a particular day?
b. If the registrar assigns a lecture hall with 500 seats for the class, what is the probability that the lecture hall overflows (i.e., strictly more than 500 attend) on a particular day?
c. To save money, the registrar wants to use an even smaller lecture hall next semester, but the professor insists on having enough seats so the probability is 95% (or more) of no overflow on a given day. How many seats does the professor need in her lecture hall?