A student works at the IT Help Desk at the Library. She works there Tuesdays and Thursdays 6 pm - 10 pm and on Sunday 1 pm - 5 pm. On average, she receives 2.4 walk-ins per shift on Tuesdays and Thursdays and 3.2 walk-ins on Sundays.

Assume walk-in arrivals occur randomly at a constant rate, and different periods of time are independent.

Assume that the proportion of walk-in problems that have a quick solution follows a Beta distribution.

1. What is the probability that our student worker will receive three walk-ins in less than two hours for a regular Sunday shift?

1. Assume = 22 and = 73. What is the expected proportion of walk-in problems that have a quick solution?

1. What is the variance of proportion of walk-in problems that have a quick solution, if = 22 and = 73?

1. If = 50, and = 25, what is the probability that tomorrow the proportion of walk-in problems that have a quick solution is more than 60%? (Use four digits after the decimal point, e.g., 0.1234)