Question

How do I solve this using excel: A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1.2, 2.4, 3.6, or 4.8 hours. The different types of malfunctions occur at the same frequency.

If required, round your answers to two decimal places.

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

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? 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?

Answer 1

a. The number Of outcomes is the duration Of service call which can be 1.2, 2.4, 3.6 or 4.8 hours, Each outcome has equal probability. Since the sum of all probabilities has to be 1, the probability of each outcome will be 0.25.

Graphical representation of the probability distribution for the duration of the service call

c. The conditions of the valid probability distribution are;

The probability of all outcomes is 0.25 which lies between 0 and 1. So first condition is satisfied. For the second condition. sum all the probabilities.

So, second condition is also satisfied. This is a valid probability distribution.

d. Probability that a service call will take 3 hours From the frequency distribution table, probability that a service call will take 3 hours is f (3) = 0.25.

e. The usual time taken by the service technician is 2.4 hours (between 3 : 00 pm and 5 : 00 pm). So probability that he has to work overtime is