Question 4

a.) Among the 60 members of the University Rugby team, 12 study in the Business School. Suppose that 10 members are to be randomly selected.

i.) If the selection is with replacement, what is the probability that

exactly five of them will study in the Business School?

ii.) If the selection is without replacement, what is the probability that exactly five of them will study in the Business School?

b.) Suppose that phone calls coming in to the student hotline of the University follow a Poisson distribution with an average rate of three calls per minute. What is the probability that:

i.) exactly three calls will come in during a particular one-minute interval?

ii.) less than or equal to two calls will come in during a particular 30-second interval?