The 30 management professors at Omega University find out that telephone calls m

Question

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 a Poisson distribution, as shown in Figure A. with an average of 1.5 calls pa minute. Because the professors spend much of their time in class and conferences, there is only a 40 percent chance that they will pick up a call themselves, as shown in Figure B. If two or more telephone calls are forwarded to the office during the same minute, only the first call will be answered.

Explanation / Answer

Time RN No. Of Calls Made RN 1st Call RN 2nd Call RN 3rd Call RN 4th Call No. Of calls not answered Assistant Idle 10:00 16 0 0 Yes 10:01 90 4 48 Yes 99 Yes 68 No 2 No 10:02 95 4 14 Yes 43 No 58 Yes 32 Yes 1 No 10:03 16 0 0 Yes 10:04 49 1 51 Yes 0 Yes

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