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NIV+RSITI
TEKNOLOGI
PETRONAS
COURSE
DATE
TIME
SMB3O23EAB2123 PROBABILITY
STATISTICS
16 MAY2008
FRIDAY)
', /
3.00PM 6.00PM
3
hours)
INSTRUCTIONS
O CANDIDATES
1.
2.
3.
4.
5.
Answer
IVE
5)
outof SIX
6) questions
rom
he
Question
ooklet.
BeginEAGH
nswer
n a new
page
n
he
Answer
Booklet.
lndicate
learly nswers
hat
arecancelled,
f
any.
Where
pplicable,how learly tepsaken n
arriving
t hesolutionsnd
indicate
LL assumptions.
Donot
open his
Question
ooklet ntil nstructed.
l t .
i i i .
There are SIXTEEN
(16)
pages
in this
Question
Booklet
Including
he
cover
page
and appendices.
Graph
paper
will
be
provided.
FormulaeBookletwill
be
provided.
Uni-versi t i
Teknoloqi PETRONAS
Note
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1.
SMB
3023
EAB
2123
a.
A
certain
machine
makes
electrical
esistors
having
a
mean
resistancef 48
ohms
and
a
standard
eviation
f 2.5
ohms.
Find
he
probability
hat
a
random
ample
f 64
of
these
esistors
ill
have
a
i.
mean
esistance
t
least
45
ohms,
[4
marksJ
ii.
mean
esistance
etween
l.S
and
4g.3
ohms,
and
iii.
total
esistance
ot
more
han
3040
ohms.
[4 marks]
[4
marksJ
b-
A
recent
urvey
f
1000
ndividuals
ndicated
hat
39.6%
f the
people
surveyed
will
vote
or
he
current
overnment
n
the
upcoming
fection
in DreamCountry.
l .
Gonstruct
99o/o
onfidence
nterval
or
the
true
proportion
f
people
hat
will
vote
or
the
current
government
n
the
upcoming
election.
[5
marks]
Use
the
confidence
nterval
n
part
(bxi)
to
test
the
hypothesis
that
he
proportion
f
people
hatvote or thecurrent overnment
is
not
4oo/o.
C
1
nef
1rv1'1'
'
62
[3
marks]
2
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SMB
3023
EAB
2123
2.
a.
Traffic
along
a
certain
city
is
being
studied.
The
daily traffic
evel
s
rated
as either
f low,
medium,
r high,
epending
n
how
many
cars
/+awI
traversqthe
street
n
a day.
The
probability
hat
an
accident
occurred
during
he
day
s
0,05.0.20
and 0.90
or
low,
medlum
or high
raffic
leVels,
espectively.
he
probability
hat
he
traffic
evet
will
be low
on
any
given
day is
twice
he
probability
hat
it
will
be medium.
The
probability
hat
the
traffic
evel
will
be
medium
s
twice
he
probability
that
t
will
be high.
i .
what is the probabilityhat he traffic evers row
on
a randomly
selected
ay?
[4
marks]
what
is
the
probability
hat
accidents
iil
occur
on
a randomty
selected
day?
[4
marks]
) : '
li
rl
i ' l
l , ; i l
i l ' l
3
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2.
SMB3023
EAB2123
b.
A tollbridge
erves
hreesuburban
esidential
istricts , B
and
C as
shown n Figure
Q2b.
During
jglgrs
of eachday,
he
Urage
volumes f vehicularraffic rom he threedistricts re 2,3, and4
vehicles
er
minute,
espectively.
ssume,that-the
eak
hour
raffic
from each district
and
the
total
peak
hour raffic
at the
toll
bridge s
a
Poisson
rocess.
\___-/
/l"ll-ttd
FIGURE
Q2b
Find
the
expected
number of vehicles
at
the toll
bridge in
1
minute.
[3
marks]
Determine
he
probability
hat more
han2 vehicleswill cross he
[4
marks]
bridge
n
1
minute
\
Find the
probability
n"t the
time
interval
between
two
consecutivears
hat cross he bridge
s
less han 20
seconds.
[5
marks]
il .
f,
F
i:
.;
I,i
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SMB3023
EAB2123
3. a.
The
article
"Hydrogeochemical
haracteristicsf Groundwater
n
a
. Mid-WesternCoastalAquiferSystem"presentsmeasurements f
various
properties
f shallow
roundwater
n a certainaquifersystem
in
re he measurementsf electrical
onductivity
in
microsiemens
er
centimetre)
or 23 samples.
Construct stem-and-leaf
lot
and
describe
ts eatures.
[6
marks]
By comparinghe mean
and median,which
measure
f central
location s
preferred?
xplain.
[4 marks]
iii. ls a histogram ppropriate
o describe
he above
data?Explain.
[2
marks]
5
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b.
SMB3023
EAB 2123
A
project
is
described
by the simple
activity network shown
in
FIGUREQ3b below,consistingof directedbranches epresenting
activities, nd nodes
representinghe
beginning
r
termination
f
activities.
Activities
and
B
are
independent ctivities
nd are scheduled
o
startsimultaneously
t day 0. Node
"a"
epresents
ompletion
f
both
activities
and B, and node
b"
represents
ompletion
f the
project.
Activity
C
can start only
when both
A and B are completed.
All
A
jurations
(in
days)
equiredor
the
respective
ctivities re normal
'( ,/ '
u , /
random
ariables s definedn eachof the
branches
n FIGURE
Q3b.
---.-
At
node
a",
activity
C
is scheduled
o
start
at day 60; howeverf there
is a de lay, t cannot
tartuntil15 days
beyond ts
scheduled
tarting
date.
, . : :v toe2
i
o^-*ol,*{
Completion
day 150
o"-w6,zs ' )
B
Day
60
DB-N(45, f i \
- l " to
(
+
tsd"ss)
fvu+
t] ,
FIGURE
3b
Find he
probability
hat
r
i. activityC will starton schedule,/i:p.,0 days after he starting
dateof
the
project.
[3
marks]
r
i i. the
project
will be comple ted n time
".Jt50
days
after he
\-/
6
starting ate.
[5
marks]
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4.
SMB3023
EAB
2123
The
average
wall hickness
f two-litre
olycarbonate
ottles s
4.0
mils.
A
quality
ontrol
engineer
akes
7 samples
of two-litre
olycarbonate
otfles
from
two
types
of bottles:
ype
A
and
type
B;
and
measures
heir
wall
thickness
in
rni s).
he
results
re
:
a, oLt:S
It
is desired
o test
the
average
hickness
f type
A
botiles
based
on
these
hypotheses:
Ho:
1t :4.9
against
Hr:
p
*
4.0
shoufd
a
/
-test
be used
o test
Ho?
lf
so,
perform
he
test
at
g5%
level
of
confidence.
f not,
explain.
[7 marks]
Construct
box
plot
or
wall hickness
f the
type
B botfles.
[5
marks]
At
957oevel
of
confidence,
s it reasonabte
o
conclude
hat
he
mean
wallthickness
f
both ypes
of
polycarbonate
ottfes
re
he
same?
Explain
our
esults.
[8
marks]
a.
b.
c.
7
8/10/2019 ProbStat - Jan 08
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SMB3023
EAB 2123
The following
ata
were collected
n B lung
cancer
patients
where
r
measureshe number fyears hepatient moke igaretteorany ormof
nicotine
roduct)
nd
y
is he
physician's
ubjective
valuationf
the
extent
of
fung
damage
n a
scale f
0
to 100.
ry
-tf l
3X-
t>
An analysis
of variance
s conducted
sing
a statisticsoftware
package
and
he
output
s displayed
n
TABLE
Q5.
TABLE Q5
The reoressionouation
s
v=21.228+1.230x
Predictor Coef
SE Coef
T
p-
value
Constant 21.228 9.442 2.248 0.066
x 1.230
0.280
4.397
0.005
S
=
8.17169
R
-
souared
R-squared(adi)=0.724
Analvsis f
Variance
Source
Df
SS
MS
F
p-
value
Regression
1
1290.84
1290.84
19.331 0.005
Residual
rror 6
400.66
66.777
Total
7
1691.50
a. Sketch scatter
plot
for
given
pairs
of
data
point
and also
plot
the
estimated
egression
ine.
[4
marks]
x
(years)
25 35
22
l5
48
39 42
3l
y (0-100)
55
60
50
30
t )
70
71
55
8/10/2019 ProbStat - Jan 08
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SMB3023
EAB2123
b. Estimate he
predicted
physician
cores,
on the
extent
of lung
damage,or wopatients hohavesmoking abits f 20 and40 years
respectively.
[3
marks]
c.
Obtain 95
%
confidencenterval
or he
rueslope
.
d.
Estimatehe
coefficientf
determinationR2).
Discuss
value btained.
e. Conducta hypothesisest on the
significance
f
levelof significance
=
0.05,
[5
marks]
briefly
n
the
[3 marks]
the
slope
at
[5
marks]
8/10/2019 ProbStat - Jan 08
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6.
SMB3023
EAB2123
A two actor
experimentalesign
was conducted
o investigatehe lifetime
of
a component
eingmanufactured,
he two
factors
are
A
(design)
nd
B
(cost
of material).
wo evels
(+)
and
(-))
of each actor
are
considered.
Threecomponenis
re manufactured
ith
eachcombination
Tdesign
nd
material, nd
he total ifetimemeasured
in
hours) s as shown
n
TABLE
Q6.
a.
A two way analysis f
variancewas
performed
o
estimate
he effects
of
design
nd
material xpense
n
the
componentifetime. omplete
the following NOVA
TABLE
QGa
by
answering
he corresponding
quest ions.Useq=0.05.
A
v0
: :
;t
f
rr
1
.l
I
i
ABLE
Q6a
fo,os.t , to
'1 ,1L
,/"
Source
DF
SS
MS
F
P-
value
lD-t
A (Design)
1
341.33 341.33
i : ' )
ty-t-
=z'b
B
(Material)
1
20t,99
21t,"9
7
s,33
{t
lnteraction
1
180 180
6t. l ,2B(
I
Error
l0
28
: .8
0
Total
11
q
o.
6b
/
x
Total
ifetime
components
(in
hours)
118
'
oh
10
8/10/2019 ProbStat - Jan 08
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SMB3023
EAB
2123
t .
Determinehe Error
degreeof freedom,
SSs,SSrot"r, Ss
and
MSerror.
,.."
,
V
marksl
ii.
Calculate
he F statistics
or B
(material)
nd nteraction.
[2
marks]
iii
Find
the
P-value
for each sources
A, B and interaction
(you
maywrite
our
answern nterval
orm).
[4
marks]
iv.
Basedon
your
esults
n
part
(a)(iii),
what
conclusionsan
you
draw
rom he actorial xperiment?
lz
-vatvt+
1 d
ro'Ll -
H,
(
*h+
cf tc+
of
a/ /
fqc-a-o. ;g
s3ntpzta+)
[2
marks]
b.
lndicate
hicheffects
re significanto the
ifetime f a component.
A,
8,
Ag
[2
marks]
c. Write he
east
quare
ittedmodelusing
nly he
significant
ources.
[3 marks]
;=
-
END OF PAPER
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