MBA 646
Professor Carter
Assignment 5
Problem 1; Ch. 4: 11; Chapter 5: 2, 9, 46, 60, 78
Problem 1 (Not in book)
The operations manager of a toll booth located at a major exit of a state turnpike is trying to
estimate the average number of vehicles that arrive at the toll booth during a one-minute period
during the peak of rush hour traffic. To estimate this average throughput value, he records the
number of vehicles that arrive over a one-minute interval commencing at the same time for each
of 250 weekdays. The data are given in the file Distribution fitting Problem 1.xlsx.
(a) Based solely on the application context, choose which model – binomial or Poisson –
you would expect to be the more appropriate one. State your reasoning.
(b) Then summarize the data with a pivot table showing a frequency distribution of number
of arrivals per minute. Obtain and print the properly labelled pivot chart. Based on the
shape, which models we have explored might be considered to represent these data?
Explain your answer.
(c) Finally, use @Risk distribution fitting to determine which discrete model is best. In the
dialog box, specify that the data are discrete and allow the default processing. Paste a
picture of the binomial and Poisson result charts from @Risk on your answer document.
ALSO, specify the parameter(s) of the two models and state which one is the better fit
based on Chi-square. What is that Chi-square value for the better model?
Note on normal distribution problems – Always sketch a normal curve showing all given
data and what needs to be found. An example of doing this on Normal Problems in Excel.xlsx
with this assignment on Blackboard. The sketch can be on paper or in Excel simply to help
you visualize the problem. Some people like to include a picture in their workbook and
document to make it easier to review later. But it is not necessary.
Note on problem 2: This provides experience in using the four Excel formulae we discussed.