Key for Sample Exam 3 - Introduction To Management | COB 291, Exams of Introduction to Business Management

Download Key for Sample Exam 3 - Introduction To Management | COB 291 and more Exams Introduction to Business Management in PDF only on Docsity! Dr. Stevens COB 291 Exam 3 Sample 2 Key for Sample Exam 3, Sample #2 (Scott Stevens) This key works the same as my others: point to the yellow block containing your answer, and I'll comment on your choice. A couple of the problems (involving drawing the decision tree and using contingency tables) work a little differently. I'll give you instructions when we get there. Scott Note that this exam contains some questions on queuing. Depending on the semester in which you take this course, the queuing material may appear on Exam 4 instead. The following exam consists of 26 questions. You may, if you wish, use a 3 x 5 notecard as an aid on this exam. The multiple choice questions, worth 3 points each, are numbered 1-23. The partial credit problems are labelled A and B. Work carefully; be sure to answer the question posed. If any question seems unclear or ambiguous to you, raise your hand, and I will try to clarify it. As usual, your scantron answer will be taken as your actual answer for multiple choice questions. You have 90 minutes to complete this test. Good luck. Maintain 4 significant digit accuracy! Point values of problems Problems 1 - 11 (Decision Trees) 3 points each (33 total) Problem A (Decision Trees) 16 points Problem B (Contingency Tables) 11 points Problems 12 (Contingency Tables) 3 points Problem 13-21 (Queuing Theory) Problems 22-24 (Expected Value) Name and Section 3 points each ( 27 points) 3 points each (9 points) 1 point 100 points Questions 1-10 deal with the scenario described below. You are going to leave work on your lunch hour to return an unwanted birthday present to ValuMart, where it was bought. ValuMart has two different stores in your area, Store A and Store B, and you may return your gift to either store. Your goal is to minimize the total (expected) time required to return to work. Store A is five minutes from your place of work. Supposing you go there, the following statistics apply. Upon your arrival, there is a 30% chance that there will be no customers at the Return Desk, a 40% chance that there will be one customer at the Return Desk, and a 30% chance that there will be two customers at the Return Desk. Assume that your total time at the Return Desk will be six minutes for each customer, including yourself. (By the way, this assumption is consistent with an assumption of exponential service time for the customers at the Return Desk.) Store B is seven minutes from your place of work. Supposing you go there, the following statistics apply. Upon your arrival, there is a 60% chance that there will be no customers at the Return Desk, and a 40% chance that there will be one customer already at the Return Desk. Again, assume that your total time at the return desk will be six minutes for each customer, including yourself. You have the option, if you wish, of checking the line situation at Store A (where the Return Desk is visible from the parking lot) and then driving onto Store B. A simple analysis of the situation will make it clear that this option is only worth consideration if the line at Store A is already two people long. This is because it takes five minutes to drive from Store A to Store B. Assume that driving time and time waiting and being served at the Return Desk are the only times which need to be considered in the problem. Remember that you must return to work! Assume that you’ll return to work by the most direct route. An abridged decision tree solution for this problem appears below. All payoffs are in minutes. Complete it by identifying what belongs in the slots marked #1 through #6b, then answer the questions below. Note that, in those questions, if an answer refers to “#1”, it means the number that belongs in slot #1, and so on. #2 #3 #5 #1 one customer ahead of you ( #6b ) 2 customers ahead of you (.3) go to Stor e A go to Store B no line u pon arriv al (.3) 1 customer ahead of you (.4) 16 22 26 no line upon arrival ( #6a ) 22.4 20 go to B #4 no one in line upon arrival (.6) 1 customer ahead of you (.4) 25.4 28 25.4 a) 67 cents/game b) $1.33/game c) $2/game d) $3.33/game e) $4/game B. (11 pts.) 90% of the students who come to class regularly pass the exam, while only 50% of those students who do not come to class regularly manage to pass. 72% of all students both come to class regularly and pass the exam. Given this information, use contingency tables below to determine how likely it is that a student who fails the exam attended class regularly. The letters in the corners of the squares are used for question #12. . (To see my answer in Word, drag your cursor to highlight the whole table, then click on the FONT COLOR button (The "A" with the colored bar under it) on the toolbar. If you’re in your browser but not in Word, you can do this same thing by highlighting the table, then choosing Format/Font/Font Color/Automatic on the menu bar.) Attend Don’t Attend Attend Don’t Attend Pass Test a 0.72 b 0.1 Pass Test d 0.72/.82 = 0.8780 0.1/0.82 = 0.1220 c 0.82 Fail Test 0.08 0.1 Fail Test 0.08/0.18= 0.4444 0.1/0.18= 0.5556 0.18 0.8 0.2 P(Row and Column) P(Column | Row) Attend Don’t Attend Pass Test e 0.9 0.5 Probability that a student who failed the exam attended class regularly = Fail Test 0.1 0.5 0.4444 P(Row | Column) Note: Original info in bold. Italicized values not needed. 12. The cell which would tell us what fraction of students passed the test is a) ab) b c) c d) d e) e Questions 13-20 deal with the scenario below. This is a queuing theory question, which is not part of the Summer 00 Exam 3 material! A large hotel has a courtesy phone in the lobby, to allow guests or visitors in the lobby to call directly to the rooms of the hotel guests. This phone is most heavily used in the early morning, between the hours 7 and 9 AM. During this time, people wishing to use the phone ("callers") arrive at a mean rate of 1 person per 40 seconds. Arrivals are Poisson distributed. The duration of the phone calls is exponentially distributed with a mean of 1 minute. Since callers are arriving faster than calls are completed, the management has seen long lines grow at the courtesy phone, which is a considerable annoyance to the callers. For this reason, the management has decided to install additional courtesy phones. To determine how many they should install, they conduct a queuing analysis of the system, considering the possibilities of having a total of 2-6 courtesy phones. It will be assumed throughout that callers will wait until a phone becomes available. The results of the analysis are shown on the next page. All times are in minutes. The tc row represents the total cost per minute of the system operation, assuming that phones cost 5 cents a minute to operate and maintain, and that customer waiting time is worth 20 cents a minute. 2 phones 3 phones 4 phones 5 phones 6 phones P(0) 0.1429 0.2105 0.2210 0.2228 0.2231 P(1) 0.2143 0.3158 0.3315 0.3342 0.3346 P(2) 0.1607 0.2368 0.2486 0.2506 0.2510 P(3) 0.1205 0.1184 0.1243 0.1253 0.1255 P(4) 0.0904 0.0592 0.0466 0.0470 0.0471 P(5) 0.0678 0.0296 0.0175 0.0141 0.0141 P(6) 0.0509 0.0148 0.0066 0.0042 0.0035 P(7) 0.0381 0.0074 0.0025 0.0013 0.0009 P(8) 0.0286 0.0037 0.0009 0.0004 0.0002 P(9) 0.0215 0.0019 0.0003 0.0001 0.0001 Pw 0.6429 0.2368 0.0746 0.0201 0.0047 Lq 1.9286 0.2368 0.0448 0.0086 0.0016 L 3.4286 1.7368 1.5448 1.5086 1.5016 Wq 1.2857 0.1579 0.0298 0.0058 0.0010 W 2.2857 1.1579 1.0298 1.0058 1.0010 tc 0.2714 0.2368 0.2772 0.3254 0.3751 13. The hotel management wants the average number of people waiting for a phone to be at most 1. What is the minimum number of phones needed to accomplish this? a) 2 b) 3 c) 4 d) 5 e) 6 14. The hotel management wants the average time that a caller waits for a phone to be no more than 15 seconds. What is the minimum number of phones needed to accomplish this? a) 2 b) 3 c) 4 d) 5 e) 6 15. The hotel management wants at least 85% of its callers to have access to a phone without waiting. What is the minimum number of phones needed to accomplish this? a) 2 b) 3 c) 4 d) 5 e) 6 16. Having three phones gives the lowest value of total operations cost, as defined in the problem. Assume the customer waiting cost remains fixed at 20 cents a minute. If the cost of maintaining and operating a phone in the lobby dropped from 5 cents a minute to 1cent a minute, the number of phones that would minimize total operations cost would now be a) 2 b) 3 c) 4 d) 5 e) 6 17. The hotel management would like to meet this condition: When a newly arrived customer does have to wait, they are usually the only person waiting for a phone at that time. (We take "usually" in thie problem to mean MORE than half of the time, and assume that the numbers given in the table are exact.) What is the minimum number of phones needed to accomplish this? a) 2 b) 3 c) 4 d) 5 e) 6 18. The value of lambda for this problem is a) 40 b) 1.5 c) 1 d) 2/3 e) .025 19 In this problem, the value of k would represent a) the number of phones in the lobby. b) the number of phones in use at a given time. c) the maximum number of people who can be waiting for phones. d) the number of people either using a phone or waiting for one. e) the number of minutes, on average, a person spends on the phone. 20. Assume, as stated in the problem, that service times are exponentially distributed with a mean of one minute. Suppose you’ve been watching a man on one of the phones, and he’s been talking for 30 seconds so far. On average, how much longer will he remain on the phone before hanging up? a) 30 seconds b) 45 seconds c) 60 seconds d) 90 seconds e) the information given does not allow us to answer the question. 21. If  = 30,  = 5, and k = 3, then (/)k/k! = a) 0 b) 1/6 c) 6 d) 6 e) 36 Problems 22-24 deal with the following situation. A normal six sided die has the following property: opposite faces on the die always add to seven. Thus, the “1” face is always opposite the “6” face, the “2” face is always opposite the “5” face, and the “3” face is always opposite the “4” face. 22. Suppose we roll a normal six sided die, then add the numbers on its top face and its bottom face. This total will a) always be seven. b) have an expected value of seven. c) have a median value of seven. d) all of the above (a-c) are true. e) none of the above (a-c) are necessarily true. 23. Suppose we take the number of the top of our normal six sided die, and multiply it by the number on the bottom. The expected value of the top is 3.5. The expected value of the bottom is 3.5. But the expected value of the top times the bottom is not 3.5  3.5 = 12.25. The reason we cannot rely on this calculation is that a) the top and the bottom value are independent. b) the top and the bottom value are different. c) the top and the bottom value are dependent. d) the top and the bottom values are symmetric; that is, we could interchange top and bottom without changing the result. e) the product of the top and bottom of the die cannot be a fractional value.