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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 166 chance of getting Heads on any single
ﬂip. 9. What is the probability that I will get no Heads at all? A) (3) (1690 (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 + "56
4 3 3) as (e Consider the following situation. We play a game where each of us rolls a fair 6sided
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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 Spring '08
 Patton
 Statistics, Normal Distribution, 0%, 2%, $0, $8, 9 w

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