BINOMIAL DISTRIBUTION PROBLEM--THE OVERBOOK MOTEL
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BINOMIAL DISTRIBUTION APPLICATION—THE OVERBOOK MOTEL
Purpose: To use the binomial distribution to analyze a business situation and provide information for managerial decisions. Use the > spreadsheet.
The Overbook Motel has 120 rooms. It is located near the main airport of a major U.S. city. Its business has no seasonality. The show-up rate averages 85% and
varies little from night to night. They have never overbooked.
A. If the motel books 120 reservations per night, no overbooking, how many rooms per night, on the average, will be unoccupied? This is a waste of the motel’s resources. If the computation results in a fraction, do NOT round to a whole number. _______________
If the average revenue per room per night is $120, what amount of revenue is LOST per year (use 365 days) due to unoccupied rooms? Again, do NOT round
the unoccupied number (if it is not a whole number). _______________
To counteract the 15% no-show rate, management is considering overbooking. They decide to overbook each night by an amount equal to the TOTAL number of
letters in your (official--as they appear on my class list) first AND last names, which is __________. If the total number of letters is less than ten (10), use ten (10.)
B. If the motel overbooks as described, how many rooms per night, on the average, will be occupied? Do NOT round to a whole number. _______________
If the average revenue per room per night is $120 what is the GAIN in revenue per year (use 365 days) due to the overbooking? Credit will be given here if it is
consistent with the previous answer. _______________
C. With the motel overbooking as described, use the spreadsheet to find the probability that, on a given night, there will be room for everyone who shows up.
This probability is: _______________
Do this in two ways.
1. Analyze in terms of no-shows. That is, let p = 0.15. Then x will be the number of NO-SHOWS. Print out an appropriate spreadsheet, label it "EXHIBIT-1" and circle the relevant probability (that you entered above). Be sure to print the heading of the spreadsheet, showing n, p, q, mean, variance, and standard deviation.
2. Analyze in terms of show-ups. That is, let p = 0.85. Then x will be the number of SHOW-UPS. Print out an appropriate spreadsheet, label it "EXHIBIT-2" and circle the relevant probability (that you entered above). With p = 0.85, change the first x-value to something in the neighborhood of 100 so that the entire distribution appears in the graph. Be sure to print the heading of the spreadsheet, showing n, p, q, mean, variance, and standard deviation.
D. Management is not pleased with the expected outcome of overbooking (the probability of everyone getting a room is too low) and wants the probability of everyone getting a room to be at least 99.5000%. How many reservations can be booked per night in order to maximize occupancy and still meet the 99.5000% requirement? _______________
Print out an appropriate spreadsheet, label it "EXHIBIT-3" and circle the relevant probability. This is a trial-and-error process in which you must try different n-values. Do it in terms of no-shows. That is, let p = 0.15. Be sure to print the heading of the spreadsheet as described above.
E. Another way to increase the probability that everyone who shows up will get a room is to make the motel larger. If management wants to use the original overbooking plan, how many rooms must be added to the motel to achieve the 99.5000% target mentioned above? _______________
Note: The answer to this one can be determined by referring to either or both of your first two computer printout pages. Circle the relevant probability on EACH of those pages (EXHIBIT-1 and EXHIBIT-2). No new printout is needed for this part.
There must be exactly THREE pages of computer printout ATTACHED to this page. Be sure to circle the relevant probability answer(s) on each page--FIVE circled probabilities in all. Use your “official” name--as it appears on my class list--on your paper. Follow ALL instructions EXACTLY. Attached exhibits should be in order: Exhibit 1, 2, 3. Your name should be in the upper right-hand corner of this page. Definition of ATTACH: to fasten with a staple or paper clip. All numbers on this page should be hand-written. Do not print the binomial-distribution graph.
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