Exam #2 Questions/Solutions

Exam #2 Questions/Solutions - Exam 2 for Math 1680 Name:...

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Unformatted text preview: Exam 2 for Math 1680 Name: Date: Directions: Circle the best answer for each question. If more than one answer is circled, you will receive no credit for that problem. _ N0 partial credit will be assigned for multiple choice problems. Normal tables and a graphic of all the 36 possible dice combinations are provided at the back ofyour test. Feel free to tear them off and use them. Good Luck! Total Score: [150 For Questions I and 2, consider the following situation. A student takes a Math 1680 exam with 15 questions. Each question has four multiple choice answers, and each question is worth 1 0 points with no partial credit given. The student decides to randomly guess an answerfor each of the questions. 1. Calculate the expected value and standard error for the student’s score (to the nearest point) on the exam out of 150 points. AM :t4points 15 dtWS w; tweet/imam: 38 i 17 points C) 150 i 0 points D) 38 i 65 points EVIS : 15(95‘32 37.5 2:38 SE 3 4.33553“ riW‘iam 2. Estimate the probability that the student will score above a 305. (Hint: use the normal table!) H “i A) 10% C) 25% D) 50% For Questions 3and 4, consider the following situation. One ticket is drawn at random from each of the two boxes below: @@i§ El 3. What is the probability that both of the numbers drawn are even? A) II 6 . Thus if: mils it, .h‘“ @331 i. ".B)——— M23 {W a” a 2 . UM, MM. sample space. 4. What is the probability that the sum of the two numbers is 6? [Me m mote seeme- For Questions 5 through 8, consider the following situation. You decide to play roulette. You bet $1 on “four numbers ”, which pays 8 to I. (In other words, you are betting that the ball will drop on one of 4 different numbers out of the 38 slots on the wheel. [fit does, you win $8. Otherwise, you lose your $1 bet.) 5. Caiculate the expected value and standard error for a single play of this ame, to the nearest cent. at? (“W iv 1-) (5 gig} fig» WW» 3 e a 35’ A) r“$5.26 i $2.76 ‘ _ B) $0.84i $2.46 ,2,” 3 gm (nth ) W Sb “9 W g i “$0.05 i $2.76 figfi “é?- 3 a; $39.“?ia 6. Assuming you are going to may, to maximize the probability that you come out ahead, you should play how many times? (Hint: what does the Law of Averages say?) L a? Manages C) 10 W D) 25 7. Suppose you play this game 16 times. What are the expected value and standard error 'n? foryourgal w “é m$gi§@ A) ~—$8.42 i $11.05 five “’ 0’ E3 i ‘2: E? ii a a if “$0. $1 :21: $1.6 $12 8. If you piayed this game 16 times, approximately what is the probability that you would come out ahead? (Hint: use the normal table!) 3%:3: '3: C) 0% D) 21% For Questions 9 and 10, consider the following situation. I flip a weighted coin 8 times. The coin is weighted so that there is a 1-66 chance of getting Heads on any single flip. 9. What is the probability that I will get no Heads at all? A) (3) (1-690 (-398 B) (55)” 10. What is the probability that I will get at least 1 Heads? (Hint: what’s the relationship between this event and the event from the previous question?) A) (3) (st (2%)? 13> be)” 11. If I deal 3 cards off of a well~shuffled standard deck, what is the probability that the first card is an eight, the second card is a king, and the third card is another king? A) (3) (3%)2 (5;) 12. If I deal 3 cards off of a well~shuffled standard deck, what is the probability that all three cards are aces? 4- 3 2 A) 5—2‘ + a + "5-6 4 3 3) as (e Consider the following situation. We play a game where each of us rolls a fair 6-sided die. If your die shows a larger number than my die shows, then you win. Otherwise (even in a tie), you lose. (For example, if you roll a 4 to my 3, then you win. If, for example, you roll a 2 to 2, then you lose.) 13. What is the probability that you win this game? 14. If I charge you $1 to play each time, how much money (to the nearest cent) should I give you for a win in order to make the game fair? W A.) 32.109 D) $0.36 15. Suppose you flip a fair coin some number of times, and you win $10 if the percentage of heads is between 45% and 55%. You would be most likely to win the $10 if you flipped how many times? A) 10 B) 50 ) .7 LOW) or? AVfl/mvgev; Formulas for General Probability: Mulrme Set Notation AB, or A n B General Rule P(A u B) = P(A) 4» ma) m P(AB) HA3) m P(A]B)P(B) Special Case, Rule Mutually Exclusive, Independent, P(A U B) x P(A) + P(B) P(AB) = P(A)P(B) Here are the 36 possible combinations of dice, mitten out for you. Tables A NORMAL TABLE 2 Height Area 0.00 39.89 0 0.05 39.84 3.99 0.10 39.69 7.97 0.15 39.45 11.92 0.20 39.10 15.85 0.25 38.67 19.74 0.30 38.14 23.58 0.35 37.52 27.37 0.40 36.83 31.08 0.45 36.05 34.73 0.50 35321 38.29 0.55 34.29 41.77 0.60 33.32 45.15 0.65 32.30 48.43 0.70 31.23 51.61 0.75 30.11 54.67 0.80 28.97 57.63 0.85 27.80 60.47 0.90 26.61 63.19 0.95 25.41 65.79 1.00 24.20 68.27 1.05 22.99 70.63 1.10 21.79 72.87 1.15 20.59 74.99 1.20 19.42 76.99 1.25 18.26 78.87 1.30 17.14 80.64 1.35 16.04 82.30 1.40 14.97 83.85 1.45 13.94 85.29 A ma (per cent) . Z 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 Height 12.95 12.00 11.09 10.23 9.40 8.63 7.90 7.21 6.56 5.96 5.40 4.88 4.40 3.96 3.55 3.17 2.83 2.52 2.24 1.98 1.75 1.54 1.36 1.19 1.04 0.91 0.79 0.69 0.60 0.51 Area 86.64 87.89 89.04 90.11 91.09 91.99 92.81 93.57 94.26 94.88 95.45 95.96 96.43 96.84 97.22 97.56 97.86 98.12 98.36 98.57 98.76 98.92 99.07 99.20 99.31 99.40 99.49 99.56 99.63 99.68 Height (parcen't) 2: Height 3.00 0.443 3.05 0.381 3.10 0.327 3.15 0.279 3.20 0.238 3.25 0.203 3.30 0.172 3.35 0.146 3.40 0.123 3.45 0.104 3.50 0.087 3.55 0.073 3.60 0.061 3.65 0.051. 3.70 0.042 3.75 0.035 3.80 0.029 3.85 0.024 3.90 0.020 3.95 0.016 4.00 0.013 4.05 0.01} 4.10 0.009 4.15 r 0.007 4.20 0.006 4.25 0.005 4.30 0.004 4.35 0.003 4.40 0.002 4.45 0.002 Area 99.730 99.771 99.806 99.837 99. 863 99.885 99.903 99.919 99.933 99.944 99.953 99.961 99.968 99.974 99.978 99. 982 99.986 99 .988 99.990 99.992 99. 9937 99.9949 99 .9959 99 .9967 99.9973 99.9979 99.9983 99. 9986 99.9989 99 .9991 ...
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Exam #2 Questions/Solutions - Exam 2 for Math 1680 Name:...

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