11. A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency

a. Develop a probability distribution for the duration of a service call.

b. Draw a graph of the probability distribution.

c. Show that your probability distribution satisfies the conditions required for a discrete probability function.

d. What is the probability a service call will take three hours?

e. A service call has just come in, but the type of malfunction is unknown. It is 3:00 p.m.
and service technicians usually get off at 5:00 p.m. What is the probability the service technician will have to work overtime to fix the machine today?