251x0431 4/20/04 ECO251 QBA1 THIRD HOUR EXAMApr 20, 2004 Name: ___KEY______________ Student Number: _____________________ Class Time (Circle) 1pm 2pmPart I: 10 points.IQs are supposedly Normally distributed with a population mean of 100 and a standard deviation of 16 16,100~ Nx. Find the following. Make diagrams!1. 4.78xP2. 6.1214.78 xP3. 2.8452.47 xP4. 6.12104.111 xP5. To get into Mensa you must be in the top 2% 0f the population. What IQ do you need? (Hint: find 02.x) the 98th percentile.251y0431 4/20/04Part II: (20+ points) Do all the following: All questions are 2 points each except as marked. Exam is normed on 50 points including take-home. (Showing your work can give partial credit on some problems! In open-ended questions it is expected. Please indicate clearly what sections of the problem you are answering and what formulas you are using. Neatness counts!)1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?a) 5 daysb) 45 daysc) 65 daysd) 81 days2. What type of probability distribution will most likely be used to analyze the number of cars with defective radios in the following problem?From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. The sales manager of one dealership wants to predict the probability that out of the 8 new cars it just received, when each is tested, no more than 2 of the cars have defective radios.a) binomial distribution.b) Poisson distribution.c) hypergeometric distribution.d) none of the above.3. A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repairon a given day, one will use what type of probability distribution?a) binomial distribution.b) Poisson distribution.c) hypergeometric distribution.d) none of the above.4. The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently. The probability that both sound an alarm in the presence of smoke is ______.5. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be at least 1 power outage in a year is ____.2251y0431 4/20/046. An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that all of the members will be men?7. The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. what is the probability that any particular cookie being inspected has at least 6.0 chip parts.8. (Dummeldinger) The amount of time between pauses on a full-screen edit terminal is uniformly distributed between 0.2 and 0.8 seconds. What is the expected (mean) pause time for the editor? [16]a) 0.4 secondsb) *0.5 secondsc) 0.6 secondsd) 0.8 secondse) 1.0 secondsf) 1.67 seconds 9. I am a real estate agent who gets an average of 1 customer every three days (31p). If I go away for three days, what is the chance that I miss a (one or more)customer?10. In problem 9, what is the chance that my first customer comes in on the third through the tenth dayafter I go away? [20]11. From an inventory of 900 new cars being shipped to local dealerships, corporate reports indicate that one-fourth have defective radios installed. What is the probability that out of the 8 new cars it just received, when each is tested, no more than 2 of the cars have defective radios?12. A concert hall has a capacity of 98 people and 100 tickets have been sold. There is a 3% probability that any given ticket-buyer will not use his/her ticket. What is the chance that everyonewho shows up will get a seat? Hint: you need the probability that 2 or more people out of100n do not come. Since you do not have tables for 03.p, show that a Poisson distribution applies and use it for your answer. (3)13. Extra credit: The geometric distribution is a special case of the negative binomial distribution. Theprobability that the thm success occurs on try x when the probability of success on any one try is p is mxmxmqpCxP11. Use this to find a) the probability of the first success on the 5th try and b) the probability of the second success on the 5th try. Show that your first result is identicalto the geometric distribution. (3) [28] 3251y0431 4/20/04 ECO251 QBA1 THIRD EXAMApr 20, 2004TAKE HOME SECTION- Name: ________KEY_____________ Student Number: _________________________Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you are using. Though I do not want typed answers, neatness counts!Part II. Do all the Following (20 Points) Show your work! Before you start find the number that we shall call a. It is the third to last digit of your student number. For example Seymour Butz’s student number is 976500, so 5a. a can be zero. 1. The table below represents the returns of two stocks. Change the table by adding a01. to .2 and subtracting a01. from .6. (Seymour changes .2 to .25 and .6 to .55.)001.006.001.002.18050901000100200yxNow find the following. a) xxE (1), b) yE (1), c) x (1), d) y (1), e) xy (1) Returnsare measured by Eand risk by the coefficient of variation, which is . Now create portfolios by letting w vary from zero to 1 by steps of .1 and saying that the return is ywwxR 1. (This stuff is done starting on page 65 of the supplement.) Compute the mean, standard deviation and coefficient of variation for each portfolio. (9) What portfolio would you recommend for a person who doesn’t care about risk, for a super cautious individual, for you, for me? Why? Write a useable report on your results. (2) [16]2. (McClave et al.) You are an inspector
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