Despite lecturing your roommates on energy conservation, there is a 60% chance that the lights in a dorm room will be left on when nobody is home. Each day is independent. Suppose that, every day the light is left on in a dorm room, there are 1000 Watts of power used. Every day when the light is turned off, there are 200 Watts of power used. You keep track of X, the number of days the lights are left on over the next 30 days.
a. What is the expected amount of power used during the 30 days?
b. Find an expression for the probability that 16,400 Watts of power are used during the 30 days. You do not need to simplify or evaluate the expression.