A technician services mailing machines at companies in the Phoenix area

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 malfunction 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 3 hours?
E. A service call has just come in, but the type of malfunction is unknown. It is 3:00 PM 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?

13. A psychologist determined that the number of sessions required to obtain the trust of a new patients is either 1, 2, or 3. Let x be random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed.

F(x) = for x = 1, 2, or 3
A. is this probability function valid? Explain
B. what is the probability that it takes exactly 2 sessions to gain the patient's trust?
C. What is the probability that it takes at least 2 sessions to gain the patient's trust?

15. The following table provides a probability distribution for the random variable x.

x f(x)

3 .25
6 .50
9 .25
A. Compute E(x), the expected value of x.

2
B. Compute , the variance of x.
C. compute , the standard deviation of x.

17. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows.

Number of service calls probability number of service calls probability
0 .10 3 .20
1 .15 4 .15
2 .30 5 .10
a. what is the expected number of service calls?
b. What is the variance in the number of service calls? What is the standard deviation?