Question

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take one, two, three, or four hours. The different types of malfunctions occur at about the same frequency. If required, round your answers to two decimal places. a. Develop a probability distribution for the duration of a service call. Duration of Callxf(x)1234 b. Select the following graph of the probability distribution.   c. Show that your probability distribution satisfies the conditions required for a discrete probability function. The input in the box below will not be graded, but may be reviewed and considered by your instructor. d. What is the probability that 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 work at 5:00 P.M. What is the probability that the service technician will have to work overtime to fix the machine today?

Answer 1

Concepts and reason

The concept of Probability distribution is used to solve this problem.

The distribution function of any real-valued random variables gives the probability value of that random variable which takes value less than or equal to a given point. The sum of the values of the probability distribution function of all the points in which it is defined is always equal to 1.

Fundamentals

If is a random variable defined in the range then the distribution function of can be defined as:

The distribution function fulfill the following properties:

(a)

Consider a technician service mailing machines at companies in the Phoenix area, depending on the type of the malfunction, the service call can be taken in one, two, three or four hours the corresponding probability is determined using probability distribution.

This is written as:

(b)

The graph shown below is wrong because the frequency axis consists the wrong value.

The graph shown below is wrong because the vertical axis shows the value and the horizontal axis shown the value of .

The graph shown below is wrong because the vertical axis shows the value and the horizontal axis shown the value of and the values of and are also wrong.

The correct graph is shown;

(c)

This can be written as;

And

(d)

The calculation of probability is:

(e)

The probability is calculated as:

Ans: Part a

The probability distribution of the service calls duration is;

Part b

The graph of probability distribution is;

Part c

The probability distribution satisfies the conditions required for a discrete probability function.

Part d

The probability that a service call will take three hours is.

Part e

The probability that the service technician will have to work overtime to fix the machine today is.

Answer 2

last one for me was 0.75