0.60 0.6 0.6 0.5 0.5 0.40 0.4 0.4 0.34 0.3 0.3 0.25 0.22 0.2 0.2 0.13 0.1 0.1 0.06 0.0 0.0 1 2 3 4 Calls Yes No Forward? 00-21 22-55 56-80 81-93 94-99 Random 00-59 60–99 Random numbers numbers (a) Probabilities of numbers of telephone calls placed per minute (b) Probability of forwarding a call Probability Probability TABLE E.5 OFFICE ASSISTANT SIMULATION 1st Call Forwarded? (Yes/No) 4th Call Forwarded? 2nd Call 3rd Call Number of Number of Forwarded? Forwarded? Calls Not Assistant Time RN Calls Made RN RN (Yes/No) RN (Yes/No) RN (Yes/No) Answered Idle (3) 10:00 68 2 30 Yes 54 Yes 1 10:01 76 2 36 Yes 32 Yes 1 10:02 68 04 Yes 07 Yes 1 10:03 98 4 08 Yes 21 Yes 28 Yes 79 No 2 10:04 25 77 No 10:05 51 1 23 Yes 10:06 67 2 22 Yes 27 Yes 1 10:07 80 87 No 06 Yes 10:08 03 10:09 03 10:10 33 1 78 No
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 is placed to the management faculty, and each telephone call consumes about one 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 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 (b). 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 a 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 a.m. Table E.5 on the following page will get you started.
c. What proportion of the time is the office assistant on the telephone? What proportion of the telephone calls is not answered? Are these proportions close to what you expected?
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