251x0831 4/16/08 ECO251 QBA1 THIRD EXAMApr 18, 2007 Name: _____________________ Student Number: _____________________Class time: _____________________ Part I. (16 points) Do all the following (2 points each unless noted otherwise). Make Diagrams! Show your work! In particular you must briefly explain how you got the answer to the value of z at the bottom ofthis page.zhas the standardized Normal distribution 1,0~ Nz for the first four problems.1. 23.1zP.2. 025.3 zP3. 07.307.3 zP4. 135.z251x0831 4/16/08 7,4~ Nx for problems 5 through 8. Note that all values of z are rounded to the nearest hundredth.5. 23.1xP6. 025.3 xP 7. 07.307.3 xP8. 135.x251x0831 4/16/08Part II: (9+ 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!) Remember that you may not be able to finish this section, so ration your time on each problem. [Numbers in brackets are a cumulative total].Justify the substitution of one distribution for another.1. A small life insurance company receives an average of five death claims a day. Assume that the Poisson distribution is correct. What is the probability that the company will receive more than 10 claims in a given day (rounded to thousandths)? (2)a) .986b) .005c) .014d) .032e) None of the above (Fill in an answer!)2. A local family planning group serves 20000 teen-age girls. It costs $50 to council each pregnant girl. There is a 5% chance that each of the 20000 girls will become pregnant during the year. Each pregnancy can be assumed an independent event. Based on what you know about the expected values of discrete distributions, how much should the agency budget for counseling this year? (2)a) $1000b) $20000c) $50000d) $100000e) None of the above.3. In the agency in problem two, 20 girls are waiting to see a counselor this morning. Half of them are pregnant. If Samantha is assigned to counsel 8 of them, what is the chance that all eight are pregnant? (I want to see your formulas and calculations – this only took me a few minutes.) (3)4. How many girls would have to be waiting before we could use the Binomial distribution to solve problem 3? (1) [8]5. OK. Assume that there are 4000 girls waiting to see a counselor and Samantha is assigned to counsel 8 ofthem, what is the chance that all eight are pregnant? The only answer that I will accept here is an answer gotten from numbers in the tables. If you just write down a solution, you will get half credit. (2)251x0831 4/16/086. A variable has the Binomial distribution. Find the following and explain how you did it.a) 5xP 02.p 200n(2)b) 60xP 40.p 200n(2 or 2.5) [14]7. Find 1711 xP for the following distribution: Continuous Uniform with ,12c 15d(1)8. If the amount of time it takes students to find a parking place has a Normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 99% of students’ search time will fall below what number? (For example it may be true that 99% take 3.6 or fewer minutes to find a parking place, but I doubt it.) (2)9. (Dummeldinger) You decide to invest in four independently moving risky stocks. You guess that each stock has an independent 40% chance of becoming a total loss. What is the chance that at least one of your stocks will tank? (2) [19]a) 0a) .0256b) .4000c) .8704d) .9744e) 1.0000251x0831 4/16/0810. (Extra Credit) The amount of rainfall in a 24 – hour period has an exponential distribution with a mean of 0.2 inches. What is the chance that a randomly picked 24-hour period will have rainfall that exceeds 0.8 inches?a) .018316b) .778801c) .221199d) .981684e) None of the above. Produce an alternate answer.251x0831 4/16/08 ECO251 QBA1 THIRD EXAMApr 24, 2008TAKE HOME SECTION- Name: _________________________ 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. Write on one side of the page!Part III. Do all the Following (25+ Points) Show your work! Neatness counts! Answers of ‘zero’ or ‘one’ especially are unacceptable without an explanation. Do not use one distribution to approximate another without justifying the replacement!1. Identify the distribution that you are using in each problem. If you have a number like gn 20, make it very clear what value of nyou are using. Look at the solved problems for Section L, the solution to Grass3 and ‘Great Distributions’ (especially the hints on the 3rd page) before you start. Let gbe the last digit of your student number. If 0g, change it to 2. Hint: It may help in these problems to realize that if 100n, 93 or more is 93 to 100 and 10 or less is 10 to zero. This is especially useful if we count failures. a. A basketball player makes %550 g of her free throws over the basketball season. In one game she gets 20 free throws and misses g13 of them. The coach will investigate if the probability of doing as badly as she did or worse is below 5%. Will the coach investigate? Do the math to justify your answer. (2)b. We believe that 80% of all accidents involve alcohol. If we investigate g6 accidents, what is the probability that g2 or fewer involve alcohol? (1)c. A test consists of g6 questions and a student must get at least 70% of the questions right to pass the course. Each question is a multiple choice question with 2 possible answers. Note that if 16n, 70% of 16 is 11.2, so 12 or more must be right. What is the probability of passing the exam if you just guess? What happens to the probability as the size of the exam increases to 20 questions? (2) Assume that the professor instead offers an exam with g6 questions with four choices and then says that a passing grade will be 50% or more. Does this raise or lower the chance of passing for the guesser? What happens to this probability as the size of the exam rises to 20? (2) d. (Dummeldinger) The diameter of ball bearings has a continuous uniform distribution over the
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