Xerox Corporation is in the information products and systems business worldwide. Everyone is familiar with the Xerox copy machines, but the company is involved in many other businesses as well. Xerox’s Multinational Documentation & Training Services (MD&TS) provides customers with timely, cost-effective, and high-quality communication services. The four basic services of MD&TS are documentation, training. translation, and publishing.
The professional writers and translators working for MD&TS use an online computerized publication system. For this system, management was interested in determining the effect of different system configurations on performance. Specifically, for a given system configuration, management was interested in determining the following:
1. The probability of a user being refused access by the system because of an excess number of users.
2. The probability of any specific number of users being on the system simultaneously.
A computer simulation model was developed for the purpose of determining these probabilities. In order to build the simulation model, it was necessary to identify the probability distribution for two key random variables:
1. The On Time per session (the length of time a user is on the system).
2. The Idle Time per session (the length of time between sessions).
Based on a survey of users, the probability distribution of on time per session was approximated as shown in the following table. Another probability distribution was developed for the random variable indicating idle time per session. These two probability distributions were key inputs to the simulation model. The results from the simulation study helped MD&TS determine a system configuration that ensured a near-zero probability that a user would be refused access to the system.
x value / probability of x
*This problem is from Anderson, Sweeney and Williams, Quantitative Methods for Business, 8e, Thompson Learning
Questions to Answer:
1. What is the expected value of the on time per session based on information given? What is your interpretation of this value?
2. What is the variance and standard deviation of this data?
3. Without assuming a particular theoretical distribution (e.g. normal) what is the probability the on time per session would be between 35 and 65 minutes? (This question is a little tricky! Hence always a good exam question.)
4. Now, with assuming a normal distribution what would your answer to #3 be — use above calculated values of the mean and standard deviation.
5. How would your answers to #1, #2 and #4 change if the above data were just nine discrete demand points. (Hint: formulas not in the text, but given in lecture.) Assume that the standard deviation is calculated by using n – 1 in the denominator.
6. What is the basic difference between ungrouped and grouped data? Explain.
7. What would be the numerical value of the range (the what? this is a trick statistics question — in the business school we don’t need to know what a range is.) under the assumption in #5?
8. Question #1 and #2 measure two moments (characteristics) of distributions. What are the other two moments of distributions.