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mid2probs - Statistics 2 Problems from past midterms...

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Page 1 Statistics 2 Problems from past midterms: midterm 2 1. (10 points) One hundred draws are made at random, with replacement, from the box: 1 1 1 1 2 Find, approximately, the chance of getting 80 1 ’s and 20 2 ’s. 2. (5 points) Ray and Bob play the following game once. A red die and a blue die are rolled. Ray pays Bob, in dollars, the number on the red die and Bob pays Ray, in dollars, the number on the blue die. Find the chance that Ray is down more than a dollar at the end of the game. 3. (10 points) A gambling house offers you the following game. A ticket is chosen at random from the box below. W I N O R P A Y U S If the letter on the ticket comes from WIN, the house gives you $1. If it comes from PAY, you must pay the house $1. If it doesn’t come from either word, no money changes hands. The ticket is returned to the box before the next play. Suppose you decide to play this game 40 times. (a) In 40 plays, your net gain will be around $__________, give or take $_______or so. (b) No money will change hands on around _______________ of the 40 plays, give or take __________ or so. 4. (5 points) A die is rolled twice. Find the chance that comes up on one roll, but not both. 5. (5 points) What is the main thing wrong with quota sampling? 6. (5 points) First one ticket, and then a second one, are drawn at random from the box shown below. The draws are made without replacement. A B C D E Find the chance the letters on the two tickets are next to each other in the alphabet.
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Page 2 7. (5 points) Box A contains 100 marbles, some are red, the rest are blue. Box B is like box A except there are twice the number of red marbles and twice the number of blue marbles. So box B contains 200 marbles. Marbles will be drawn one at a time, at random, from one of the two boxes. You are given two choices: (a) 100 draws with replacement will be made from box A. (b) 200 draws with replacement will be made from box B. After you make the choice, the draws are made from the box you chose, and you win a dollar if the number of times a red marble comes up in the draws is the same as the number of red marbles in the box. Check ( ) one of the four options below. _____ (a) gives a better chance of winning. _____ (a) gives a smaller chance of winning. _____ (a) and (b) give the same chance of winning. _____ Can’t tell without more information. State your reasoning. 8. (5 points) Studies often involve taking a sample from a population. True or false, and explain: “In most such studies the investigator can decide, by examining the sample carefully, whether or not it is a representative cross-section of the population for the variables under investigation.” 9.
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