A technician services mailing machines at companies in the Phoenix area. Dependi

Question

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1.1, 2.3, 3.2, or 4.1 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. Duration of Call x f(x) 1.1 2.3 3.2 4.1 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below. Does this probability distribution satisfy equation (5.1)? Does this probability distribution satisfy equation (5.2)? What is the probability a randomly selected service call will take 3.2 hours? 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?

Explanation / Answer

Since, the different types of malfunctions occur at the same frequency, let us assume that the frequency for each is a constant 'k'. Now we can construct the frequency distribution of the number of calls 'x' as:

Now the probability distribution of 'X', the random variable denoting the  is given by:

The probability a randomly selected service call will take 3.2 hours= Pr[X=3.2] = 1/4=0.25

Probability the service technician will have to work overtime to fix the machine

= Probability that he stays for more than (5-3=2) hours

= Pr[X>2]

=Pr[X=2.3] + Pr[X=3.2] + Pr[X=4.1]

=3/4 = 0.75

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