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Unformatted text preview: STOR 155, 881, 2011, Midterm Exam 2 (6/6/11) Name: PID: Instructions: Both the exam and the bubble sheet will be collected. 0n the bubble sheet, print
your name and ID number, Sign the honor pledge, also bubble in your name and ID number.
Each question has only one correct choice (decimals may need rounding). Use #2 pencil only (do
not use ink) to ﬁll bubble completely. No notes or remarks are accepted. Do not tear or fold the bubble sheet. A grade zero will be assigned for the entire exam if the bubble sheet is not ﬁiled out according to
the above instructions. ' 1. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B
are independent, then
(1) P(A and B) = 0.016
(2) P(A or B) = 1.0
(3) P(A and B) = 1.0
(4) 'P(A or B) z 0.84 2. Belgium has two ofﬁcial languages — French and Dutch. Assume that about 60% of the
people speak Dutch and 40% of the people speak French. Deﬁne the event A as the
event that two randomly selected Belgians speak the same language. What is the complement of event A? (1) 0.48 (2) 0.52 (3) {Dutch, French} (4) {(Dutch, French), (French, Dutch)} 3. Ignoring twins and other multiple births, assume babies born at a hospital are
independent events with the probability that a baby is a boy and the probability that a
baby is a girl both equal to 0.5. What is the probability that at least one of the next three babies is a boy?
(1) 0.125
(2) 0.333
(3) 0.750
(4) 0.875 Page 1 Use the following to answer questions 4—5: Consider the following probability histogram for a discrete random variable X. 4. This probability histogram corresponds to which of the following distributions forX'?
(1) Value ofX 1 2 3 4 5
Probability 0.06 0.25 0.38 0.25 0.06 (2) ValneofX 1 2 3 4 5
Probability 0.10 0.25 0.30 0.20 0.15 (3) Value ofX l 2 3 4 5
Probability 0.10 0.25 0.30 0.25 0.10 (4) None of the above. 5. What is P(X< 3)?
(1) 0.10
(2) 0.25
(3) 0.35
(4) 0.65 Page 2 Use the foilowing to answer question 6: The probability density of a continuous random variable X is given in the ﬁgure below. 0 l 2 X 6. Based on this density, what is the probability that X< 0.5 orX> 1.5?
(1) 1/3
(2) %
(3) % 3‘
(4) 1 ' a Use the following to answer questions 78: Suppose there are three balls in a box. On one of the balls is the number 1, on another is the
number 2, and on the third is the number 3. You seiect two balis at random and without
replacement from the box and note the two numbers observed. The sample space S consists of g
the three equally likely outcomes {(1, 2), (l, 3), (2, 3)} (disregarding order). LetX be the sum
of the two bails selected. 7. Which'of the following is the correct distribution for X? (1)
Value of}?
Probability .1/3 3’3 3’3
(2)
Value ofX
Probability 3 ya ya
(3)
Value ofX l 2 3
Probability 2,5” 34 3%;
(4)
Value of}? Probabiiity if; 3% 1% Page 3 8. What is the probabiiity that the sum is at least 4?
(1) 0
(2) 1/3
(3) 2/3
(4) 1 Use the following to answer questions 9—10: A smali store keeps track of X= the number of customers who make a purchase during the ﬁrst
hour that the store is open each day. Based on the records, X has the following probability distribution. Value of X 0 l 2 3 4
Probability 0.1 0.1 0.1 0.1 0.6 9. What is the mean number of customers who make a purchase during the first hour that
the store is open?
(1) 2.0
(2) 2.5
(3) 3.0
(4) 4.0 10. What is the standard deviation of the number of customers who make a purchase during
the ﬁrst hour that the store is open?
(1) 1.4
(2) 2.0
(3) 3.0
(4) 4.0 Use the following to answer questions 11 — 12: When ﬁgure skaters need to find a partner for “pair ﬁgure skating,” it is important to find a
partner who is compatible in weight. The weight of ﬁgure skaters can be modeled by a normal
distribution. For male skaters, the mean is 170 lbs. with a standard deviation of 10 lbs. For
female skaters, the mean is 110 lbs. with a standard deviation of 5 lbs. Let the random variables
X = the weight of female skaters, Y: the weight of male skaters, and W = YmX : the weight
difference between male and female skaters. ' 11. Suppose we consider the weights of the male partner and the female partner to be
independent. What is the standard deviation of the random variable W?
(1) a“. : 3.871bs. '
(2) 0",: 11.18 lbs.
(3) a... = 14.21 lbs.
(4) 01.: 15 lbs. Page 4 12. It does not seem likety that the weights of the male partner and the female partner would 13. be independent. If the correlation pbetweenX and 1’ equals 077, what is the standard
deviation of the random variable W? (l) 0...:693 lbs.
(2) o...=11.181bs.
(3) a...=14.211bs.
(4) 03,.2151138. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) e 0.3.
What is' P(A c or B c )? ‘ (r) 0.40 (2) 0.49 (3) 0.91 (4) 1.40 Use the following to answer questions 14 —~ 15: Bob has recently been hired by a shop downtown to help customers with various computer
related problems. Lately, two different viruses have been bugging many customers —— virus
Dummy and virus Smarty. It is estimated that about 65% of the customers with virus. problems
are bothered by virus Dummy and the remaining 35% by virus Smarty. If the computer is
infected by virus Dummy, Bob has a 90% chance of fixing the problem. However, if the
computer is infected by the virus Smarty, this chance is only 70%. 14. 15. A virusinfected computer is randomly selected from the shop. It is infected with virus
Dummy. What is the probability that it cannot be ﬁxed by Bob? (I) 0.10 (2) 0.30 (3) 0.35 (4) 0.65 If a virus—infected computer is randomly selected from the shop, and we know it was
ﬁxed by Bob, what is the probability that it was infected with virus Dummy? (1) 0.078 (2) 0.650 (3) 0.705 (4) 0.783 Page 5 Use the following to answer questions 16—47: The Biology Department plans to recruit a new faculty member. Data collected by a different
university on the 410 possible candidates is available. The Biology Department is debating to put
a requirement of 10 years of teaching experience in the job advertisement. The available data on
the candidates is shown below: Less than 10 years i0 or more years experience experience Total
Male 1 78 1 12 290
Female ' 99 21 120
Total 277 1 33 41 0 16. What is the conditional probability that a female candidate has less than 10 years
experience?
(1) 99/410; (2) 99/120; (3) 99/277 17. Are the events F 2 {candidate is female} and E = {candidate has less than 10 years
experience} independent?
( 1) Yes; (2) No; (3) cannot be determined. 18. In a certain game of chance, your chances of winning are 0.2. Assume outcomes are
independent and that you will play the game five times.
Suppose it costs $1 to play the game. if you win, y0u receive $4 (for a net gain of $3).
If you lose, you receive nothing (for a net loss of $1). What are your expected (net)
returns for a round of ﬁve games? (1) $3; (2)$0; (3)W$I; (4) $2 19. A college basketball player is known to make 80% of his free throws.
At the end of a game, his team is losing by two points. He is fouled attempting a three—
point shot and is awarded three free throws. Assuming each free throw is independent,
what is the probability that he makes at least two of the free throws?
(i) 0.384
'(2) 0.64
(3) 0.80
(4) 0.896 Page 6 20. John’s birthday is March 21 whiie Mary’s birthday is April 22. What is the probability
that at least one of John’s two younger brothers share birthday(s) with John 01' Mary?
(1) 1  2 x (363/365)
(2) 1 ~ (363/365) x (363/365)
(3) 1 — (363/365) x (362/365) Use the following to answer questions 2lm22: Birth weights of babies follow roughly a normal distribution with mean 7 lbs. and standard
deviation 14 oz. (1 lb. : 16 02.). 21. Dr. Watts has 4 deliveries. What is the probability that all 4 babies weigh more than 7.5 ibs? '
(1) 0.0065; (2) 0.1265; (3) 0.2839; (4) 0.4848 22. What is the probability that the average weight of the 4 babies weigh more than 7.5 lbs?
(1) 0.0065; (2) 0.1265; (3) 0.2839; (4) 0.4848 23. A onequestion survey is to be distributed to a random sample of adults in Ohio.
Suppose 40% of all adults in Ohio support Issue A. How Earge of a sample would be needed
To guarantee that the standard deviation of the sample proportion of Issue A supporters is
less than 0.01?
(1) 100; (2) 1000; (3) 1500; (4) 2400 Page 7 24. A soft drink machine can be regulated so that it discharges an average of 5.5 ounces per cup.
1f the ounces of ﬁll are normally distributed with a standard deviation 0, what value should a be so that with probability 0.015 a'S—oz cup wili overﬂow?
(1) 1 (2) 0.23 (3) 1.2 (4) 0.05 25. if a student has a GPA 3.0 or higher, she has a chance 0.8 of getting in a preferable major;
with a GPA lower than 3.0, the chance will drop to 0.2. Suppose 20% of the students have their
GPA‘s “2 3.0”. If Frank fails to get in his preferable major, what is the probability that his GPA is 3.0 or higher?
(1) 4/5 (2) 5/18 (3) 1/17 (4)1/5 26. A Tar Heel basketball player makes 80% of his free throw attempts. Among 3 attempts he
has, the probability that he at least misses one is equal to (1)61/125 (2)48/125 (3)124/125 (4) 2/3 27. A stack of :1 cards contains 2 red cards and 2 black cards. Randomly draw two cards without
replacement. Consider the events A : {the lst draw is black} and B : {the 2nd draw is red}. Then A and B are (1) mutually exclusive (2) complements (3) independent (4) none of the above 28. A college basketball player makes 80% of his free throws. At the end of a game, his team is
trailing by two points, and he is fouled when attempting a threepoint shot. Hence he is awarded 3
free throws. Assume independence among outcomes of different free throws. What is the probability that his team wins the game? (1)0.64 (2) 0.512 (3) 0.104 (4) 0.896 Table entry for z is
theareaunderthe
standard normai curve to the left of z. .0003
.0005
.0007
.0010
.0013
.0019 '
.0026
.0035
.0047
.0062
.0082
.0107
.0139
.0179
.0228
.0287
.0359
.0446
.0548
.0668
.0808
.0968
.1151
.1357
.1587
011.41..
.2119
.2420
.2743
.3085
.3446
.3821
.4207
.4602
.5000 .0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.0045
.0060
.0080
.0104
.0136
.0174 .0222  .0331
.0351
.0436
.0537
.0655
.0793
.0951
.1131
.1335
.1562
.1314
.2090
.2339
.2709
.3050
.3409
.3733
.4163
.4562
.4960 .0005
.0006 .0009
.0013
.0018
.0024
.0033
.0044
.0059
.0078
.0102
.0132
.0170
.0217
.0274
.0344
.0427
.0526
.0643
.0778
.0934
.1112
.1314
.1539 .1788‘ .2061
.2358
.2676
L3015
.3372
.3745
.4129
.4522 Probability w ‘*.E!I‘u"v"F’k‘Ithjﬁﬁiﬁﬁﬁﬁfég‘RrH'€;'ﬂiiﬁh ==‘~:. 42" "’33": "1’2‘:“—.'3.—2~.'sii3!£ ., .0322 .0003 .0003
.0004 .0004
.0006 .0006
.0003 .0003
.0011 .0011
.0016 .0015
.0022 .0021
.00 0~ . .0029
.0 40 1.0039
.0054 .0052
.0071 .0069
.0094 .0091
.0122 .0119
.0153 .0154
.0202 .0197
.0256 .0250
.0314 ".0401 .. .0392
 .0495 .0435
.0606 .0594
.0735 .0721
.0335 .0869
.1056 .1033
.1251 .1230
.1469 .1446
.1711 .1635
.1977 .1949
.2266 .2236
.2573 .2546
.2912 .2377
.3264 .3228
.3632 .3594
.4013i .3974
.44 4“"~ .4364
.40 1? 54761 .0004
.0005
.0008
.0011
.0015
.0021
.0028
.0038
.0051
.0068
.0089
.0116
.0150
.0192
.0244
.0307
.0384
.0475
.0582
.0708
.0853
.1020
.1210
.1423
.1660 .1922 . .2206
.2514
.2843
.3192
.3557
.3936
.4325 .0003
.0004
.0005
.0007
.0010
.0014
.0020
.0027
.0037
.0049
.0066
.0087
.0113
.0146
.0188
.0239
.0301
.0375
.0465
.0571
.0694
.0838
.1003
.1190
.1401
.1635
.1894
.2177
.2483
.2810
.3156
.3520
.3897
.4286
.4681 .0002
.0003
.0005
.0007
.0010
.0014
.0019
.0026
.0036
.0043
.0064
.0034
.0110
.0143
.0133
.0233
.0294
.0367
.0455
.0559
.0631 .0323
.0935
.1170
.1379
.1611 .1367
.2143
.2451 .2776
.3121 .3433 .3359 .4247 .4641 Table entry for z is the
area under the
standard normal curve
to the Staff: of z. .02 .03 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359
.5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753
.5832 .5871 .5910 .5948 .5987 .6026 ..6064 .6103 .6141
.6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517
.6591 .6628 .6664 W%.6700 , _q§7§6 .6772 .6808 .6844 .6879
.6950 .6985 ,.7019 '3g27054 :;§;7088_ .7123 .7157 .7190 .7224
.7291 .7324 .7357 , .7389 ’ '.7422 .7454 _ 5393; 7517 .7549
.7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852
.7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133
.8186 .8212 .39238. .8264 .8289. .8315 .8340 .8365 .8389
.8438 .8461 .8485 .8508 .8531  .8554 .8577 . .8599 .8621
.8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830
.8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015
.9049 .9066 .9082 $ .9099 j#19115 .9131 .9147 .9162 .9177
.9207d .9222 .9236 .9251 f“?§{9205“ .9279 .9292 .9306 .9319
.9345 .9357 .9370 .9382_; :Egggg:) .9406 .9418 .9429 .9441
.9463 .9474 .9484 .9495 '  .9515 .9525 .9535 .9545
.9564 .9573 .9582 ..9591 .9599 29608 .9616 .9625 .9633
.9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706
.9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767
.9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817
.9826 .9830 .9834 .9838 .9842 '.9846 .9850 .9854 .9857
.9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
.9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916
.9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936
.9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952
.9955 .9956 .9957 .9959 .9960 .9961 .9962. .9963 .9964
.9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974
.9975 .9976 .9977 ‘.9977 .9978 .9979 .9979 .9980 .9981
.9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 .9987 .9987 .9988 » c.9988 ' . 1 ,..‘ f .er19989 .9989 .9989 .9990 .9990
.9991 .9991 .9991 .149999‘1v849992. .9992 .9992 .9993 .9993 .9993 .9994 .9994' .9994’ '.9994 .9994 .9995 .9995 .9995
.9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997 .9997 .9997 .9997 .9997 .9997 .999? .9997 .9997 .9993 O
I
2
3
0
1
2
3
4 U'lhhbJNF‘O ChmhbJND—‘O DOH10\m13WNNO Namawwwo Entry is P(X : k) z ( H k )p" (1 — p)” Tabtes T—7 (Confirmed) m1: ' ...
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This note was uploaded on 11/18/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Summer '08 term at UNC.
 Summer '08
 AndrewB.Nobel

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