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Unformatted text preview: 1. Harris recently installed a spam ﬁlter software, but he still saw spam emails in his
inbox. He made a daily record of the number of spam emails that were delivered to
his inbox over the past 20 days. The following is a frequency histogram for his data.
The frequency refers to the number of days. histogram of spam email data Frequency
3 c, III
I—rwmrw—T'm—r—I 20 40 60 80 100 120 if: spam emails a) Harris also plotted a stemplot for the data. Which of the following is a correct
stemplot for his data? Check only one answer. [2 marks} 1“ Stemplot A _StemplotB _StemplotC A. 2 I 011355 B. 2 I 011355 C. 1 I 05
3 I 01467 3 I 01467 2 I 011355
4 I 12479 4 I 12479 3 I 01467
5 I 56 5 I 56 4 I 12479
6  8  0 5  56
7 I 10 I 5 6 l
8 I 0 7 l
9 I 8 I 0
10 l 5 b) What is the third quartile of the number of spam emails? Use the stemplot you
have chosen in part (a) to answer this question. Check only one answer. [2 marks] _ 23
w 25
47 \/ 48 2. Consider the following two studies: Study 1: A study compared 120 patients with brain cancer to 246 healthy patients
without brain cancer. The patients’ cell phone use was measured using a question—
naire. The brain cancer patients used cell phones more often, on the average. Study 2: A study exposed rats to two common types of cell phone radiation for four
hours a day, ﬁve days a week, for two years. One third of the rats were randomized to
be exposed to analog cell phone frequency, one third to digital cell phone frequency, 
and one third served as controls and received no radiation. At the end of two years,
their brains were examined for cancerous tumors. No statistically signiﬁcant difference
in the percentage of brain cancer was found among the groups. a) True or false? Study 1 shows that cell phone use causes brain cancer. [2 marks]
_True L False b) Identify the following elements for Study 2: i. the experimental unit [2 marks]: (1. Fat ii. the factor [2 marks]: “12‘ng 0f radtahon iii. the treatments [3 marks]: .0 . an new; fr wan ch H'Ql cell Ywm Wes Win 0:) 3. A city council was planning to turn a major street in the city from a primary traffic
artery to a secondary traﬁic artery. It sent out a questionnaire to all the 36,589
households living in the city requesting for their input concerning the plan. Thirty
four percent of the 10,375 households who returned the questionnaires Opposed the
plan. For the following statements, check all that are correct. [3 marks] \/ This survey conducted by the city council is likely to suffer from nonreSponse bias. _ The 10,375 households that returned the questionnaires formed a random sample
of the population. __ The percentage of the 10,375 households that opposed the plan, 34%, is a param—
eter. 4. You need to drive past two trafﬁc lights on the way from your house to the nearest
grocery store. The probability that you hit a red light is 0.5 at the ﬁrst intersection
and 0.4 at the second intersection. The probability that you run into a red light at
both intersections is 0.25. On a random day you drive from home to that grocery store. Deﬁne the following events: E1 : you run into a red light at the ﬁrst intersection
E; w you run into a red light at the second intersection
E3 2 you run into a green light at both intersections
E4 = you run into a red light at both intersections Which of the following statements is (are) true about the above events? Check all that
are correct. [6 marks] E1 and E2 are independent events.
E1 and E2 are disjoint events.
'\/ E3 and E; are disjoint events. E3 is the complement of E4. 5. You draw two cards without replacement from a deck of 52 cards. If the ﬁrst card
is not a spade, ﬁnd the probability that the two cards drawn are both diamonds. [6 marks] Deane Events «. A : the ﬁrst card draLUn IS 0 Spam;
Di 2 +he 13+“ Card dream Is a drummed , 621,2
19(Dgand Dal AC)
to PM
' PM")
a HEre PCB; and D7. and AC) 15 the, pmbabilltkj 0F ge’rhng a diamond
on ma 4116+ draw (who GM'l‘Oma‘lTlcalLtj saﬁstses not {act Wat H’ ‘5 not a spade) and also a diamond (m m sewnd draw:
7..
1.8“ 9091004 D?) : H90 7“ PCDleQ: Eva 1—
‘3  éﬂ
G PLA‘) :2 \la PUD: \—§§  52
l3 t7 4+
6 d ‘— = *— X...— en  .__
lean DzlA) (51 51) 51 _ 51 6. The length of trout in a lake is normally distributed with mean ,u = 0.95 feet and an
unknown standard deviation 0‘. If 60% of all trout are longer than 0.8 feet, what is the
value of a? [6 marks] Le’r X: length 01¢ a trout IV N(}i:.o,¢16 43(7) 0“)
90% 09 all «tvoui (ll/UL [ranger Haan 018105
39 PCX > 0:8) 3 QloO
0.8 \S the. 40th Permllo.‘
£40 (Lioen puma oil; a MNLonD . 0.3 *i"
O.%~ﬂ O.% OHS
Oi: : .. 7. In a university parking database with 5600 registered vehicles, records show that 43%
of the registered vehicles are Asian makes, 23% are Eur0pean makes and the remaining
are American makes. Among all the 5600 cars, 20% once received a parking ticket. a) You randomly pick three vehicles with replacement from the database. What is
the probability that at most two of the three are American makes? [6 marks] Lei— X= ii Pimencan cats Del 0? «He; 3 chosen
XN Em (n: 3, P: 1— 0.43~ 0.23 = 0.34) P( (3+ most 2 out 093) are WCGIYL mama) :P(Xé9_)
spasm + For:1) + PCX=Z> :: (3)0‘340Li—oﬁ4ls + (3’) 0.34‘ (Pose? + (3) 034200340 b) Consider a random sample of 100 vehicles selected from the database. The sample proportion of the 100 selected vehicles that had never received a park
ing ticket has an approximate 95% chance of falling between
0 \q'l and O ‘. g8 . Fill in the blanks and Show your calculation below. [4 marks] LE”? P : POPUthicm Proportion OF 0016 that wager FQCUVCCl W a, Pom/ting micei I 1‘ 0.20 3' O. 80 sampm propomom all Cars (owl 0? 100) +h6d‘ never A
p I
received CL priming +ioke+ No+ez rip: 100(080): 807:0 , arr—p)=20>ro p Fol Hows the normal dISf'T’lbul‘lCm appmilmaielﬂ m+h mean: 08 and SD 3 /09(l—os) :: 004—
100 35 tens—mat. rule, We middle 962’ OF diverage
will be over the Marvel: 0. 8 :t 2 (0.04)
=37 (0.2112J 083) 5 8. Two stores sell watermelons. At the ﬁrst store the melons weigh an average of 20
pounds with a standard deviation of 2.2 pounds. The melons are sold for 36 cents a
pound. At the second store the melons are smaller, with a mean of 17 pounds and
a standard deviation of 2 pounds. The store is having a sale on watermelons — only
25 cents a pound. Assume that the weights are normally distributed. Jenny selects a
melon at random at each store. Find the mean and the variance of the difference in
the prices Jenny pays for the two melons. [6 marks] Let X: weight 0? a nUZJOn 190m Firs+ store
Y 2: u u v: u ‘I generic! Store EUR) : 20 J $13M): 2.7 Eif) Z \zl' ) SD (‘1): 2 Diﬁﬁremo. in mm prices bcmenn W 2 Melons
:2: D = (3‘be —' OQSY (in doilaws) 5(1)): s(o.se><e 052630
2 0.349 EH) , 0.25 EH) : O.3Q>(20) _. 0.2504) c $2.,‘i5 VCD) : v (0.3(OX— 0.25%) :— ass2 vcx) + 0.25?" WY) [It makes seme to assume the. welg lots 0?
"the, 2 muons are mole/pended] _—_ 0.351(21‘“) + 0.251(2“)
:2 0.8773 dollars?" 9. Each day the value of a particular stock goes up one unit with probability 0.3, stays
the same with probability 0.5 01' else goes down one unit with probability 0.2. Taking
changes over consecutive days to be independent of each other, estimate the probability
that the stock will have increased by a value of at least five units over 500 days. [10 marks] Let X: GMOtin'l 0? change on a dag
probability (ﬁnish 0;. X \5 0C The overall change over 500 claids 2
Y: X1+Xz+.. wasn't to ﬁnd (SLY?) S) Poms)
. 5‘ — 3N X ;we ”0‘00
q\ :2." ptw _,_.. _,
..— s tau/ls ~th some) 'l'xsw How is 35 distribmted? 7? Wm be @mein moi/ma} b3 ctT( $300730) 3'4" €193” MM: 509: 0.1% 5’00 (3(17/ .. 2.875)
1otoozo O‘i‘ig (Lowell O,?/f56'0 600: Z 2. ﬂ ><'=7C)
: ~1.(o.2)+ C(05)
+1 (03)
z + 0.1
vcx): see)  (Em)?
.2 ixleoeag—a (oiu’l
: Lei)2(oxz) +02m5)
+12 (0.3)_o.01 Misterm B Soiuhonkeﬂ 1. Circle the most appropriate answer: [2 marks each] a) Form a data set that consists of four integer numbers from 1 to 10 (inclusive,
without repeats). Among all the possible data sets that can be formed (as described in the above),
which of the following statements is NOT correct?
1. The set of numbers 1, 2, 3, 4 gives the smallest possible standard deviation.
ii. The set of numbers 4, 5, 6, 7 gives the smallest possible standard deviation. The set of numbers 1, 5, 6, 10 gives the largest possible standard deviation.
iv. The set of numbers 1, 2, 9, 10 gives the largest possible standard deviation. b) The length of a ball of yarn is a random variable with mean 150 ft and standard
deviation 2 ft. The variance of the total length of three randomly chosen balls of
yarn will be iii. 18 ft?
iv. 36 ft2 0) Sixty—four percent of the teenager population is nearsighted. Consider random
samples of 4 teenagers drawn from this population. The following are three state
ments about the sampling distribution of the sample proportion (of 4 teenagers)
who do not suffer from nearsightedness. (I) The sampling distribution has a mean of 36%.
(II) The sampling distribution has a standard deviation of 24%.
(III) The sampling distribution follows the normal distribution approximately. Which of the above statements is (are) correct? 1. Statement (1) only. .Statements (I) and (II) only. iii. All the three statements.
iv. None of the three statements. cl) There are two urns. Each urn contains 1 black marble and 2 white marbles. You
randomly draw one marble from each urn. Let X be the number of white marbles
out of the two being drawn. Then ©X is a Bin(2,=§) random variable.
ii. X is a Bin(3,§) random variable.
iii. X is a Bin(6,%) random variable.
iv. X is not a Binomial random variable. 2. The following boxplots show left hand lengths. The boxplot on the left shows data
from left handers. The boxplot on the right shows data from right handers. Leﬁ hand size (inch) Left Right handedness Which of the following statements is (are) correct about the distributions of the left
hand size data for the two handedness groups? Check all that apply. [4 marks] i The distribution among the right handers is skewed to the right. For the distribution among the right handers, the ﬁrst quartile is the same as the
third quartile. _ The left and right handers have roughly the same mean left band size. m More than 25% of the left handers have left hand sizes that are shorter than the
minimum left hand size of the right handers. 3. A farmer wants to study the effect of plant density on tomato yields. He buys two
varieties of tomato plants: A and B — 24 each. He then randomizes the 24 plants of va
riety A to one of the three density choices: 4 plants/m2, 6 plants/m2 and 8 plants/m2.
He does the same to the 24 plants of variety B. At harvest, he measures the yield (in
kilograms) of each tomato plant. Identify the following components of the farmer’s experiment to study the effect of
plant density: [12 marks] a) experimental units: ”:0 make Plants b) factor(s) (how many and list it / them all):
1 iactor 2 plant densrtg c) levels of each factor (how many and what are they?): 3 levels 03? plan+ denSitg = 4: b, 5 plants/m? d) treatments (how many and what are they?): 3 treatments . 4, (a, 8 plants [m1 e) response variable:
weld 0? a tomato plant f) design type (check only one): _ completely randomized design
_V_’_ randomized block design
matched pairs design Which of the following is (are) involved in the experiment? Check all that apply. L Replication.
______ Confouding. A control group. 4. Your friend, Carl, has been doing a research project about the coffee drinking habit of
UBC students. Last Wednesday during 7:30—8:30 am, he stood next to the Starbucks
coffee counter in the SUB and interviewed all students who bought coffee there. Carl asked each student two questions:
1. How many cups of coffee do you drink daily?
2. Do you have an early morning class (an 8am or 9am class)? Carl found that the average number of cups of coffee these interviewed students drink
daily is 1.78. a) The students interviewed by Carl formed (check only one): [2 marks] w a simple random sample.
.1“ a convenience sample. _ a stratiﬁed random sample.
_ a multistage sample. b) The average number of cups of coffee consumed daily by the interviewed students,
1.78, is (check only one): [2 marks] a population.
__ a sample.
a parameter. i a statistic. c) Do you think the average number of cups of coffee, 1.78, provides a reliable esti
mate of the true mean daily coffee consumption of all students in UBC? Briefly
explain why or why not. [2 marks] NoJ Carl‘s sample Suffers 140m true, problem 03C
uedercovemge. Students who clen’Jr dnnk cofFee
were not m+emewed at: all. “rm average, 1.4a)
overesumoleo «em m mum dang coeFee COiﬁsumPthGn. 5. The following table shows the breakdown of the annual salaries of university graduates
and the proportion of graduates falling in each income category. Annual salary range Proportion of university graduates under $20k
$20k to $40k $40k to $60k
$60k to $100k
above $100k a) A university graduate is randomly chosen. Here are two events: Event A : The chosen graduate has an annual salary under $20k.
Event B : The chosen graduate has an annual salary under $40k. Are the two events independent? mYes LNG
Explain your reasoning. [4 marks] PM) = 0‘5 Pte) = 0. 15+ one :OJoO I”? A has occurred) 8 must“ have, occurred, in other
words, Tm OCCALn‘enCQ 0? A ham altered “hm pmbablld‘g ol— e (Fae) :odooj white News: :1. J and terms. pcgmﬂ
Pu [5 are not mdeperrdam. 9E PM and: s) 2 ms 4: PM» He) _— 0,15% o.(oo:0,oq b) Two university graduates are chosen at random. What is the probability that
one has an annual salary under $20k and the other has an annual salary between $20k and $60k? [6 marks} Deﬁne. 2 events ~.
AL : salanj 15 Under $20K {for the My inleldLLal 8i “ salomj as baweem $2034 and $60K JR» Jam. Hh main/amt PCA‘: = OAS HBO—"0.454: 0.50:0;75 C21,; PL 3A. and 913 OR {Au and 0.3)
.W,«{’ cligjoﬁ'ﬁg J
:PKPH and Dz) + P( A; 0nd Di) b3 acidihb‘n 'ruﬂe
 PlA\)7LW91) + P(A2}%9(Di) be} WQMCM‘IGH (uQQ Qg th’ .— ; 0,154. 0775+ 0&6 s OTIS 1 mdmaunﬂa Should
”40.17.5 5 ba lndwpmdwct, W8 was“: «ea rises”fixemwiﬂ “€348 pmiﬂiéhili'ﬁjl c) A random sample of 400 university graduates is drawn from all university grad— uates. 3 Approximate! the probability that 180 or fewer of the sampled graduates
earn more than $40k annually. State any assumption(s) you have made in the calculation. [7 marks] Let x: #9rnduanas and of 400 who earn > $40!: annually.
X“) Brn(n=4oo, p: o.30+o.oq+o,or :olqo) we use normal appmxtmaj’zon +0 1%. Bmmma! chock Ccmdmons: (I) we have at random sample at graduate:
(2) n: 400 < 5% OF populaton Size (41! graduate) {3) npf 400(Oi4‘) 2160710) ”(115) 2329:0710
Xa’efm'M (ft = rip: Ibo) Valnpﬂrp‘): 677474361)
p(><.~:—:so) : p(x< teas) {— cementing Wmm :: {3(52. :1 {80.9429 :: P(% (ZCCI) 50.9814 6. At the present time the noise level per jet takeoff in one neighbourhood near the airport
is believed to follow the normal distribution with mean 102 decibels and standard
deviation 5 decibels. Suppose a regulation is passed that requires jet noise in this
neighbourhood to be lower than 105 decibels 95% of the time. How much should the
mean noise level be lowered to comply with the regulation? [6 marks} 1.8+ X = neisa level under the reguiation N N ( )JLNEW )Q':5) i 0 T
_ d 0
Want X be 4 105 E) 96/ 0F +M 41mg @530!” 0’
to. P(x< i055) : 0,015 is unchanged,
105 as is "the. 95th pertenﬁte». ‘ ,arfi «2g
“ 3 ix
3% = [a score 130?" area: 0.95]
z . 4 .. .
l b 5 #NEi/J lOS y
C. qu ___ lOSuFNEW
o“ 6
New = :03.— on zqg : 105~ 5x Halts = crewrs as "no mean hOISQ. level should be. lowered by
(102— Qbﬂ'rS“ ) =2 5.225 d6. 7. According to a research study of ﬁsh in the Tennessee River, the weights of ﬁsh in the
river follow the normal distribution with mean 950 grams and standard deviation 180
grams. a) True or false? The average weight of a random sample of 36 ﬁsh drawn from the
Tennessee River follows the normal distribution. This is a result of the Central
Limit Theorem. [2 marks] m True
“ﬂ False b) Find the probability that a random sample of 36 ﬁsh drawn from the Tennessee
River has an average weight of at least 980 grams. [5 marks] Let X: weighir a? a i’iSlA N NCﬂ=¢i503 ) 6:180:33
74 : average magi/1+ OF Big Fish m NCME‘JQSO‘B) lESO .
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Piiaqeo‘) " (it
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‘Pl 3:0 77 so )
; Pl’Z 7 :L
’ 3 a g
r; L (1— ObﬁD b9 515° ate
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 Spring '08
 KARIM

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