The 30 management professors at Omega University find out that telephone calls made to their offices are not being picked up. A call-forwarding system redirects calls to the management office after the fourth ring. A department office assistant answers the telephone and takes messages. An average of 90’telephone calls per hour are placed to the management faculty and each telephone call consumes about 1 minute of the assistant’s time. The calls arrive to Poisson distribution, as shown in Figure with an average of 1.5 calls per minute. Because the professors spend much of their time in class and in conferences, there is only a 40 percent chance that they will pick up a call themselves, as shown in Figure. If two or more telephone calls are forwarded to the office during the same minute, only the first call will be answered.

a. Without using simulation, make preliminary guess of what proportion of the time the assistant will be on the telephone and what proportion of the telephone calls will not be answered.

b. Now use random numbers to simulate the situation for one hour starting at 10:00 AM. Table will get you started,

a. Probabilities of numbers of telephone calls placed per minute

b. Probability of forwarding a call

c. What proportion of the time is the office assistant on the telephone? What proportions of the telephone calls are not answered? Are these proportions close to what you expected?

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0.6 0.5E 0.4 0.34 0.3 0.25 0.22 0.2 0.13 0.1 0.06 0.0 1. 22-55 4. 94-99 Calls Random numbers 00-21 56-80 81-93 (a) Probabilities of numbers of telephone calls placed per minute 0.60 0.6 0.5 0.40 0.4 0.3 0.2 0.1 0.0 Yes 00-59 No 60-99 Forward? Random numbers (b) Probability of forwarding a call Probability Probability