And the probability is _______. [14.5]251x0621 3/4/06ECO251 QBA1 SECOND HOUR EXAMMarch 22 and 23, 2006 Name: _____________________ Student Number: _____________________Hour of Class Registered: Circle MWF1, MWF2, TR12:30, TR2:00There will be a penalty if you do not provide all this information! Part I: (3 points) 2 point penalty for not trying.The scores of a sample of statistics exams are (with extra credit included) as below. Find the sample standard deviation. Show your work!97 86 106 87 104 102 98 95 76 99 2x910361251x0621 3/4/06Part II: (35 points+) Do all the following: All questions are 2 points each except as marked. Exam is normed on 50 points including take-home. [Bracketed numbers are a point total] If you answer ‘None of the above’ in any question, you should provide an alternative answer and explain why. You may receive credit for this even if you are wrong.1. If events A and B are mutually exclusive and their probabilities are not zero, the following cannotbe true.a) A and B are independent events.b) A and B are complements.c) Neither of the above can be true.d) Both of the above can be true.2. If events A and B are independent, 3.AP and 5.BPwhat is BAP ?a) .80.b) .15c) .20d) .65e) None of the above.f) Not enough information to tell.3. If ,3.AP 5.BP and 4.BAP, what is BAP ?a) .80.b) .15c) .12d) .20e) None of the above. [6]2251x0621 3/4/06Questions 4-7 are based on exhibit 1.Exhibit 1: A fast food restaurant has its outlets distributed as follows. (Dummeldinger). A restaurant is to be chosen at random to test market a new menu item. RegionNE SE SW NWCityPopulationBelow 10000A.05 .06 .03 .0010000-100000B.15 .15 .05Above100000C.20 .04 .10 .054. Fill in the missing number (1)5. What is the probability that, if we select a restaurant at random, we pick a restaurant that is in a city of below 10000 or one that is in the Southeast. (2.5)a) SEAP b) SEAP c) SEAPd) ASEPe) None of the above.And the probability is _________________.6. What is the probability that, if we select a restaurant in a city of below 10000 at random, we pick a restaurant that is in the Southeast. (2.5)a) SEAP b) SEAP c) SEAPd) ASEPe) None of the above.And the probability is _________________.7. What is the probability that, if we select a restaurant at random, we pick a restaurant that is in a city of below 10000 and is in the Southeast. (2.5)a) SEAP b) SEAP c) SEAPd) ASEPe) None of the above. And the probability is _______. [14.5]3251x0621 3/4/068. You and two of your friends are shooting arrows at a target. Each of you has an independent probability of hitting the target of 70%. What is the probability that all three of you will hit the target?9. You and two of your friends are shooting arrows at a target. Each of you has an independent probability of hitting the target of 70%. What is the probability that at least one of you will hit thetarget? [18.5]10. You and two of your friends are shooting arrows at a target. Each of you has an independent probability of hitting the target of 70%. Let x be the number of individuals that hit the target. Do the following:a) Find the distribution of x. (Show what values x can take, what the probability of each value is, and demonstrate that we have a valid distribution.) (6) If you cannot do this problem you may make up a reasonable distribution to do b), c) and d). Warning – this problem could take a while to do. If time is a constraint for you, skip it and come back to it later.b) Find 2F, the cumulative probability ( 2xP) (2)c) Find the expected value and variance of x. (3)d) Using the mean and variance that you found in c) , If you and your buddies as a group paid $10 to shoot and the operator of the game gives your group $5 for each hit on the target, what is the expected value and variance of your winnings? (3) [32.5]4251x0621 3/4/0611. You are dealt 6 cards from a deck of 53 cards containing 4 each of 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 10s, jacks, queens kings and aces, 13 each of hearts, diamonds, spades and clubs and one joker. What is the probability that your hand contains the joker? (4) You must work this out all the way to get full credit and at least show how many possible hands there are.12. You are dealt 6 cards from a deck of 53 cards containing 4 each of 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s,10s, jacks, queens kings and aces, 13 each of hearts, diamonds, spades and clubs and one joker. What is the probability that your hand contains three hearts? (2.5) This can be left in factorial form. 13. You are dealt 6 cards from a deck of 53 cards containing 4 each of 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s,10s, jacks, queens kings and aces, 13 each of hearts, diamonds, spades and clubs and one joker. What is the probability that your hand contains at least one heart? (2.5) This can be left in factorial form. [41.5]14. Assume that z is a standardized variable and that 317 zy. The standard deviation ofy is: (2.5) [44]a) -17.b) -14c) 17d) 289e) 51f) Not enough information.g) None of the above.5251x0621 3/4/06 (Blank)6251x0621 3/4/06 ECO251 QBA1 SECOND EXAMMarch 22 and 23, 2006TAKE HOME SECTION- Name: _________________________ Student Number: _________________________Throughout this exam show your work! Neatness counts! Please indicate clearly what sections of the problem you are answering and what formulas you are using. Part III. Do all the Following (12+ Points) Show your work! 1. (5 points)row x xQ 1 -4 5 2 -3 5 3 -2 10 4 -1 .. 5 0 10 6 1 5 7 2 5 Make yourself an individualized distribution as follows. Take the six digits of your student number and add them to the numbers in xQ.Divide the result by 100 to get a column of numbers and fill in the missing number to get a valid distribution. row x xQ nostu xQ' xP 1 -4 5 9 14 0.14 2 -3 5 9 14 0.14 3 -2 10 9 19 0.19 4 -1 .. . .. .... 5 0 10 9 19 0.19 6 1 5 9 14 0.14 7 2 5 9 14 0.14For example, assume that my student number is 999999. I have written it in the column labeled ‘stu no’ and then added it to xQ to get the column xQ'. Then I divided the result by 100 and filled in the missing number in
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