QUESTION 5 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 the same frequency (i.e., any service call will need either 1 hour or 2 hours or 3 hours or 4 hours with equal chance). Do not round your answers. Develop a probability distribution for the duration of a service call. Let X be the random variable for the duration of a service call and f(X) be the probability distribution X 1 12 3 4 2. Consider the following two required conditions for a discrete probability function: (i) f(x)>=0 (greater than or equal to zero) for all possible values of X (ii) Summation of f(X) for all possible values of X is equal to one. Does this probability distribution satisfy condition (i)? Type "Yes" or "No" Does this probability distribution satisfy condition (ii)? Type Yes" or "No" 3. What is the probability a service call will take 2 hours? f(x) 4. A service call has just come in but the type of maifunction is unknown. It is 3:00 PM and service technicians usually get off at 4:30 PM. If the service needs to be finished today, what is the probability that the service technician will have to work overtime to fix the machine today?