Problem 1
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.